FOR BETTER UNDERSTANDING
THE CARET SIGN (^) MEANS RAISE TO POWER

Index (indices) in Maths is the power or exponent which is raised to a number or a variable. The plural form of index is indices. In algebra, we come across constants and variables. The constant is a value which cannot be changed. Whereas a variable quantity can be assigned by any number or we can say its value can be changed. In algebra, we deal with indices in terms of numbers. Let us learn the laws/rules of the indices along with formulas and solved examples.

Index (raise to power) Definition

A number or a variable may have an index. Index of a variable (or a constant) is a value that is raised to the power of the variable. The indices are also known as powers or exponents. It shows the number of times a given number has to be multiplied. It is represented in the form:

a^m= a × a × a ×……× a (m times)

Here, a is the base and m is the index.

The index says that a particular number (or base) is to be multiplied by itself, the number of times equal to the index raised to it. It is a compressed method of writing big numbers and calculations.

Example:  2³ = 2 × 2 × 2 = 8

In the example, 2 is the base and 3 is the index.

Laws of Indices

There are some fundamental rules or laws of indices which are necessary to understand before we start dealing with indices. These laws are used while performing algebraic operations on indices and while solving the algebraic expressions, including it.

Rule 1: If a constant or variable has index as ‘0’, then the result will be equal to one, regardless of any base value.

a⁰ = 1

Example: 5⁰ = 1, 12⁰ = 1, y⁰= 1

Rule 2: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable.

a-² = 1/a²

Example: 5-¹ = ⅕, 8-³=1/8³

Rule 3: To multiply two variables with the same base, we need to add its powers and raise them to that base.

a² × a³ = a²+³

Example: 5²×5³ = 5²+³ = 5⁵

Rule 4: To divide two variables with the same base, we need to subtract the power of denominator from the power of numerator and raise it to that base.

A³ ÷A² = A³-²  =A¹

Example: 10⁴/10² = 10⁴-² = 10²

Rule 5: When a variable with some index is again raised with different index, then both the indices are multiplied together raised to the power of the same base.

(A²)³ = A²×³

Example: (8²)³= 8²×³= 8⁶

Rule 6: When two variables with different bases, but same indices are multiplied together, we have to multiply its base and raise the same index to multiplied variables.

A^p×B^p= (AB)^p

Example: 3²×5² = (3 x 5)² = 15²

Rule 7: When two variables with different bases, but same indices are divided, we are required to divide the bases and raise the same index to it.

a^p/b^p = (a/b)p

Example: 3²/5² = (⅗)2

Rule 8: An index in the form of a fraction can be represented as the radical form.

A^p/q = q√A^p

Example: 6^½ = √6

If you can solve this, then you have no problem
Just an example
Find the value of 272/3.

Solution: 27^2/3

= 3√27²

= 3√3^³(²)
Here The index power of 3 will break the cube root, therefore
You have
3²which will equal
= 9

Download why! Official music video by dablixx osha

How to Earn Money As a Freelancer

Author Info

Last Updated: June 9, 2020 References ApprovedDownload Article

Freelancing means to have different jobs or short-term assignments or contracts with number of companies, websites, organizations, etc., without any long-term contract. The Internet has greatly expanded opportunities to earn money working as a freelancer. Approximately 10.3 million Americans work for themselves, a number that is expected to grow in the future.^[1] Freelancing can be freeing, as the name suggests, as well as empowering and challenginghttps://googleads.g.doubleclick.net/pagead/ads?guci=2.2.0.0.2.2.0.0&client=ca-pub-9543332082073187&output=html&h=120&slotname=8943394577&adk=1906044181&adf=2802691016&pi=t.ma~as.8943394577&w=360&lmt=1610362529&psa=0&channel=8567383174%2C7928712280%2C6429618073%2C2001974826&format=360×120&url=https%3A%2F%2Fwww.wikihow.com%2FEarn-Money-As-a-Freelancer&flash=0&wgl=1&dt=1610445453191&bpp=40&bdt=783&idt=1339&shv=r20210107&cbv=r20190131&ptt=9&saldr=aa&abxe=1&correlator=5998636418767&frm=20&pv=2&ga_vid=1029555206.1610445455&ga_sid=1610445455&ga_hid=907794479&ga_fc=0&ga_cid=amp-UuiVWU2Jyk4FPutfEpeFzw&u_tz=60&u_his=6&u_java=0&u_h=780&u_w=360&u_ah=780&u_aw=360&u_cd=24&u_nplug=0&u_nmime=0&adx=0&ady=508&biw=360&bih=644&scr_x=0&scr_y=38&eid=21068769%2C21069719%2C21066819%2C21066973&oid=3&pvsid=3081995340311819&pem=406&ref=https%3A%2F%2Fwww.wikihow.com%2FwikiHowTo%3Fsearch%3DHow%2Bto%2Bearn%2Bmoney%2Bonline&rx=0&eae=0&fc=896&brdim=0%2C0%2C0%2C0%2C360%2C0%2C360%2C644%2C360%2C644&vis=1&rsz=%7C%7CpeE%7C&abl=CS&pfx=0&fu=8192&bc=31&ifi=1&uci=a!1&fsb=1&xpc=kVQvTjGX2Y&p=https%3A//www.wikihow.com&dtd=1465

Method 1 of 2:Becoming a Freelancer

1. 1Decide on your craft. Decide what type of freelance work you are committed to doing. Freelancing jobs are as broad as the work force, and you need identify what it is you want to do before you can begin to do it. View your skills as valuable resources that are worth charging and receiving pay for.^[2]https://googleads.g.doubleclick.net/pagead/ads?guci=2.2.0.0.2.2.0.0&client=ca-pub-9543332082073187&output=html&h=250&slotname=7710650179&adk=1764630173&adf=364481383&pi=t.ma~as.7710650179&w=310&lmt=1610362529&rafmt=12&psa=0&channel=8567383174%2C7928712280%2C6429618073&format=310×250&url=https%3A%2F%2Fwww.wikihow.com%2FEarn-Money-As-a-Freelancer&flash=0&wgl=1&dt=1610445453335&bpp=31&bdt=927&idt=1384&shv=r20210107&cbv=r20190131&ptt=9&saldr=aa&abxe=1&prev_fmts=360×120&correlator=5998636418767&pv_ch=8567383174%2B7928712280%2B6429618073%2B&frm=20&pv=1&ga_vid=1029555206.1610445455&ga_sid=1610445455&ga_hid=907794479&ga_fc=0&ga_cid=amp-UuiVWU2Jyk4FPutfEpeFzw&u_tz=60&u_his=6&u_java=0&u_h=780&u_w=360&u_ah=780&u_aw=360&u_cd=24&u_nplug=0&u_nmime=0&adx=25&ady=1195&biw=360&bih=644&scr_x=0&scr_y=48&eid=21068769%2C21069719%2C21066819%2C21066973&oid=3&pvsid=3081995340311819&pem=406&ref=https%3A%2F%2Fwww.wikihow.com%2FwikiHowTo%3Fsearch%3DHow%2Bto%2Bearn%2Bmoney%2Bonline&rx=0&eae=0&fc=896&brdim=0%2C0%2C0%2C0%2C360%2C0%2C360%2C644%2C360%2C644&vis=1&rsz=%7C%7CpeEbr%7C&abl=CS&pfx=0&fu=8448&bc=31&ifi=2&uci=a!2&btvi=1&fsb=1&xpc=y3LMzCS27F&p=https%3A//www.wikihow.com&dtd=1420Advertisement

It is however important to know that you do not need to fear changing you area of focus as a freelancer. Many freelancers start doing something and through the journey of freelancing they discover that they are actually good and love something entirely different. Know that you can always change no matter what.

1. 1
   • Reflect on what you’re good at. Just about every type of skill can be turned into a freelancing opportunity. Keep in mind that you’re “secondary” skills, like researching and writing, for example, can be just as useful as a specific set of skills unique to a profession (e.g., graphic designer or computer programming). If you know you’re a strong writer, then you could develop a freelance writing business.
   • It’s very easy to believe that you don’t have the necessary skills or experience, but in fact you actually need very little experience in order to get started freelancing. Instead, believe in your abilities and focus on producing good work.^[3]
2. 2Create a brand. To get your freelancing operation off the ground and becoming profitable, you need to think about how you will market yourself and your products/work. This is called branding. You need to create a brand for your what you’re selling and how it sets you apart from the competition – this is your “identity and includes your website, logo, tagline, blog, and social media accounts, among other aspects.
   • Your brand should clearly communicate what you do that is special and what you offer that is worth buying. Try to narrow your focus to a specific industry. For example, if you decide you want to do freelance writing, you might only decide to write for online travel sites and business and thus be a freelance travel writer. Or you might decide you want to write for business and corporate websites. Specializing within the field (in this case, the very broad field of writing) will make you more attractive to potential clients because it shows you have a particular rather than a generic set of skills, also known as a niche.^[4]
   • However, don’t let the brand be your primary focus. You could have a huge Instagram or Twitter following, but that doesn’t really pay the bills. Don’t worry about followers or retweets, and instead focusing on producing quality work. That’s the ultimate way to build your freelancing business and earn money.^[5]
3. 3Build a portfolio showcasing your work. A lot of potential clients are less interested in your specific qualifications than in a demonstrated ability to do the job. They want to see samples of your work and decide whether you’re a good fit for their particular project. So building a strong portfolio of your work (samples as well as past projects) is key to building your business and in fact, you shouldn’t launch your freelancing business until you have this portfolio. Include as well testimonials of people and organizations who you’ve worked with. Reading glowing reviews will help boost your profile among prospective clients.^[6]
   • Generating submissions for your portfolio takes time and resources. If you have no paid assignments or previous work to put in a portfolio, create some by offering your services pro bono or taking your free time to produce some.^[7]
   • Remember that more is not always better. Although volume can be good and help with self-promotion, it’s also important to try to incorporate some bigger and higher profile jobs, rather than just building a portfolio full of the smallest and least lucrative projects. If you want to make big money by working with high-paying clients, then you need to show those clients that you can produce the kind of work they’re looking for. Again, consider offering pro bono when you’re first starting out.^[8]
   • Don’t launch your freelancing career until you’ve actually created the products or provided the services you plan to sell. Having the portfolio shows clients that you’ve actually done what you’re telling them you can do.^[9]
4. 4Develop business-savvy skills. You may be a freelancer, but you also need to be a business man or woman. To successfully earn money as a freelancer and turn it into a career, you need to become familiar with the basics of operating a business, like taxes, bookkeeping, marketing, etc. In many cases, these business basics will take more time than the actual freelance service or product you offer!^[10]
   • Consider talking to friends (in real life or online) who’ve earned money freelancing about the business ins and outs. You could also consult a number of books and online sites about how to start up a business from the ground.
   • Although it might seem premature to worry about the “business” of your freelance work, having a business model with goals, deliverables, benchmarks, and so on can help you determine the scope and scale of your freelancing operation. A clear business model, and transparent accounts and books, will also show clients that you’re the real deal – a professional freelancer and not just someone working in their pajamas at home.
5. 5Set up an invoicing system. Part of doing freelancing as a way to earn real money means setting up a system for charging and receiving payment. Before you reach out to potential clients and start actually doing the freelancing work, be ready for it. It’s a lot easier to keep up with accounting and invoicing along the way, rather than leaving it until later on or even until the dreaded tax season. Create a financial framework that will make it easy for you to keep organized financial money. Doing this will also help you track how much money you’re earning and whether you’re making a profit.^[11] Consider doing the following:
   • Set prices for the services or products you offer. Figure out if you charge an hourly rate or per piece/product. Be ready to explain how you charge for what you’re offering (i.e., the breakdown).
   • Create invoice templates. Using a word-processing tool (like Microsoft Excel, for example), design an invoice that has all of the important information (service rendered, cost, payment, addresses of the payee and payer, etc.).
   • Establish an accounting plan and consider opening up a business bank account. Often banks have special services and fees for business bank accounts.
   • Look into how much you should be charging and setting aside for taxes.
6. 6Get paying clients. Once you have a portfolio, it’s time to get out there and start pitching to clients. Freelancing successfully is a numbers game — the more potential clients you locate and reach out, the more likely you are to get work and, most importantly, get paid.^[12] You can begin by tapping into your personal network of family, friends, and old coworkers. Ask them for referrals; this can help bring in some startup work that can get your freelancing operation off the ground. However, you’ll also need to make the first move and branch out in a lot of cases in order to earn good money. When pitching your product or services to new clients, pitch only to those clients who are relevant. And pitch to a lot of them.
   • Try the 10-before-10 rule; pitch to 10 potential clients before 10 in the morning during the work week.^[13]
   • If you’re still working other jobs, set aside some of your free time to starting building up a client network that you can draw on in the future.
   • You should know who your target clients are if you’ve branded yourself properly. Remember that businesses want to work with freelancers who seem like their services/products were designed just for the needs of those businesses. The concept of specialization, mentioned above, creates this sense.^[14]
   • You could also try using a freelance market. There are several online freelance marketplaces like Elance and oDesk, where you can offer your services and look up and pitch to clients. These can be very useful for freelancers just starting out.^[15]
   https://googleads.g.doubleclick.net/pagead/ads?guci=2.2.0.0.2.2.0.0&client=ca-pub-9543332082073187&output=html&h=250&slotname=7710650179&adk=1124698307&adf=2230045593&pi=t.ma~as.7710650179&w=310&lmt=1610362529&rafmt=12&psa=1&channel=8567383174%2C7928712280%2C6429618073&format=310×250&url=https%3A%2F%2Fwww.wikihow.com%2FEarn-Money-As-a-Freelancer%23&flash=0&wgl=1&adsid=ChAIgK71_wUQ6IWZwuXf7sAlEj0ApDDKKAhWof16RgvWia-UF3eZ4_GHLh-J_VdhOarNhymii12TdI-MxJ09Zp5I4YI_ZzZ9p2NR6rTRe3P7&dt=1610445502416&bpp=27&bdt=50008&idt=31&shv=r20210107&cbv=r20190131&ptt=9&saldr=aa&abxe=1&cookie=ID%3Ddac16e2b158065a1-2253a4389da600cd%3AT%3D1610445476%3ART%3D1610445476%3AS%3DALNI_MaL3v9l6WY8yHgOko8y5Q2O–goMQ&prev_fmts=360×120%2C310x250%2C0x0&nras=1&correlator=5998636418767&pv_ch=8567383174%2B7928712280%2B6429618073%2B&frm=20&pv=1&ga_vid=1029555206.1610445455&ga_sid=1610445455&ga_hid=907794479&ga_fc=0&ga_cid=amp-UuiVWU2Jyk4FPutfEpeFzw&u_tz=60&u_his=7&u_java=0&u_h=780&u_w=360&u_ah=780&u_aw=360&u_cd=24&u_nplug=0&u_nmime=0&adx=25&ady=8482&biw=360&bih=644&scr_x=0&scr_y=8469&eid=21068769%2C21069719%2C21066819%2C21066973&oid=3&psts=AGkb-H_gjufGXOfijwil5yPQLNkrczc75KZ8CRn4WzxucY5whNm18AOOCr6Vu7XeQLU&pvsid=3081995340311819&pem=406&ref=https%3A%2F%2Fwww.wikihow.com%2FwikiHowTo%3Fsearch%3DHow%2Bto%2Bearn%2Bmoney%2Bonline&rx=0&eae=0&fc=896&brdim=0%2C0%2C0%2C0%2C360%2C0%2C360%2C644%2C360%2C644&vis=1&rsz=%7C%7CpeE%7C&abl=CS&pfx=0&fu=8448&bc=31&ifi=3&uci=a!3&fsb=1&xpc=ZpbmYtmWtZ&p=https%3A//www.wikihow.com&dtd=67Advertisement

Method 2 of 2:Understanding Freelance Work

1. 1Have a vision. Know what you want and go for it! The biggest obstacle to freelancing is overcoming that mental blockage that says “You can’t do it and you shouldn’t.” To overcome that feeling, show yourself that it freelancing isn’t just something you want to do because you want to work from home, but a business plan. This isn’t just a fantastical idea, but a business reality.^[16]
   • One useful way to start seeing freelancing as a viable option is to being the process of legitimizing it. Come up with a name for your business and a logo or font-type. Once you start creating the vision, it becomes easier to realize that this a real business you’re launching. Start the process by establishing a business name and creating a vision for your company brand.
2. 2Take time to enter into freelancing. Don’t jump right in and hedge all your bets on freelancing right away. Freelancing can be a great way to earn money, but it can also take a considerable amount of time to build up. Make sure that you are 100% committed to investing your time and effort into freelancing before you decide to quite your other job(s).^[17]
   • Keep in mind that a lot of the steps in Part 1 can be undertaken while you are still working at your day job. Focus on setting the ground plan for freelancing while still earning a stable income and you’ll feel more confident and comfortable taking the leap.
3. 3Be ready for slow periods. In every business, there are slow periods. This will happen for your freelancing operation as well. You’ll probably get stressed and think the whole thing is a flop but know that all industries always go through ebbs and flows. Also know that eventually, business will pick back up.
   • Make sure to plan for slow periods, whether that meanings changing prices or having a savings plan.
   • The more you freelance, you’ll be able to identify trends and peak and slow periods. Ultimately, you’ll be able to anticipate when things slow for you and you’ll stop getting worried because this will be routine.^[18] and you can start to expect the drought and prepare. But it takes a while to get there.
4. 4Be prepared to hold yourself accountable. Since as a freelancer, you are your own boss, you need to make sure that you’re doing what you need to do. While most people get excited at the prospect of not having a boss looking over their shoulders, it’s also important to remember that bosses keep you motivated and give you feedback on your progress. Without a boss, you’ll need to do this yourself most of the time.^[19]
   • Engage in daily and weekly reflection about the work you’ve done to make sur you’re hitting your targets. If you’re not, then you need to have a serious look at your work habits and system.
   • Other people – such as editors or mentors if you’re a freelance writer, for example – can also help provide accountability. At the end of the day, however you’re the boss so be the boss.
5. 5Be ready to talk about yourself a lot. As a freelancer, especially a newly minted one, you’ll have to talk about yourself, what you do and what you’ve done A LOT. You are your own marketer. Opportunities can come from surprising and unexpected places, so it’s important that you have a ready pitch of a few sentences about yourself and your freelancing services or products that you can use whether you’re at a holiday party or business fair. If you’re a private person by nature, try writing down and practicing the pitch until it becomes natural. Over time, you’ll get better at talking about yourself and doing self promotion. A little bit of hustling is essential to success in the freelancing world.^[20]
   • Make sure to get business cards made so you can hand them out whenever you bump into someone and start chatting. These are an old – but still relevant – way to get your name out there.
6. 6Cope effectively with being alone. The lack of social interaction and communication of the office environment can make freelancers feel lonely and isolated.^[21] While you’ll need to learn how to stay goal-directed and on task without the motivation of others, you should also take care to prevent loneliness from taking root. Try working in different spaces a day or two a week; take your computer to a local coffee shop and work there. Even just hearing the buzz of social interaction can make you feel less alone. ^[22]
   • You could also meet up with other freelancers for lunch or coffee to discuss problems, concerns, and other topics. There are a number of local business networking groups that can help connect people who work for themselves and usually remotely.^[23]
   • There are also little things you can do to relieve feelings of isolation. Call someone, instead of sending an email, for example.^[24]