How To Find Raise To Power

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Exponents are used when a number is multiplied by itself. Instead of writing out ${\displaystyle four*iv*4*four*4}$ , nonetheless, yous tin can simply write out ${\displaystyle iv^{five}}$ . This is explained in the "Solving Bones Exponents" method below. Exponents brand it easier to write out long or circuitous expressions or equations, and you tin also easily add together and decrease exponents for simplifying problems as needed, when you lot have learned the rules (for example: ${\displaystyle iv^{2}*4^{3}=4^{5}}$ ). Annotation: If y'all're looking to solve exponential equations, such as ${\displaystyle ii^{2x}=thirty}$ , click hither, for when the exponent includes an unknown.

1. 1

   Learn the right words and vocabulary for exponent issues. When yous have an exponent, like ${\displaystyle two^{three}}$ , you accept two simple parts. The bottom number, hither a two, is the base of operations. The number it is raised to, here a 3, is known as the exponent or power. If yous are talking most ${\displaystyle 2^{three}}$ , yous would say information technology is "two to the third," "2 to the third power," or "two raised to the third ability."

   • If a number is raised to the 2nd ability, similar ${\displaystyle 5^{2}}$ , you tin also say that the number is squared, such every bit "5 squared."
   • If a number is raised to the third power, similar ${\displaystyle ten^{iii}}$ , you can also say it is cubed, such as "ten cubed."
   • If a number has no exponent shown, similar a simple 4, information technology is technically to the kickoff power and tin be rewritten as ${\displaystyle four^{1}}$ .
   • If the exponent is 0, and a "non-null number" is raised to the "zero power", then the whole thing equals 1, such as ${\displaystyle 4^{0}=i}$ or even something like ${\displaystyle (3/8)^{0}=1.}$ At that place is more well-nigh this in the "Tips" section.

2. 2

   Multiply the base repeatedly for the number of factors represented by the exponent. If you need to solve an exponent past paw, starting time past rewriting information technology as a multiplication problem. You want to multiply the base by itself for the number of the exponent. So, if you accept ${\displaystyle iii^{4}}$ you would multiply three in a series of four dissever factors, or ${\displaystyle three*three*3*iii}$ . More than examples include:

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3. 3

   Solve an expression: Multiply the first two numbers to get the product. For example, with ${\displaystyle four^{5}}$ , you'd beginning with ${\displaystyle 4*4*iv*4*4}$ This looks daunting, but just have it 1 step at a fourth dimension. Start by multiplying the first two fours. And so replace the two fours with the answer as shown here:

4. iv

   Multiply that answer to your first pair (xvi hither) by the next number. Keep multiplying in the numbers to "abound" your exponent. Standing our example, you would multiple 16 by the next iv, and then that:

5. 5

   Try your manus with a few more than examples, checking your answers with a computer.

6. 6

   Utilise the "exp," " $$ 10 northward {\displaystyle x^{n}} " or "^" button on a calculator to do exponents. It is nigh incommunicable to exercise larger exponents, similar ${\displaystyle 9^{fifteen}}$ by hand, simply calculators tin handle it with ease. The button is ordinarily clearly labeled. The Windows Seven reckoner tool tin can be changed to scientific figurer style by clicking the "View" tab of the estimator and selecting "Scientific". When you desire the standard calculator way back, use "View" and select "Standard".

   • Google the expression to cheque your answer. Yous tin can utilize the "^" button on your calculator, tablet or smart phone keyboard to input an expression into Google search, which will spit out an instant answer, and suggest similar expressions to explore.

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1. i

2. ii

   Multiply numbers with the same base by calculation the exponents together. If y'all take ii exponents with the aforementioned bass, such every bit ${\displaystyle x^{2}*x^{5}}$ , all you have to practice is add the two exponents together with the aforementioned base. Thus, ${\displaystyle ten^{2}*ten^{5}=x^{7}}$ .^[iii] If you lot're confused, just break it downwardly into all of it's parts to effigy out the system:

3. 3

4. four

   Care for negative exponents like fractions, or the number's reciprocal. If you don't know what reciprocals are, it is okay. If you accept a negative exponent, similar ${\displaystyle 3^{-2}}$ , simply make the exponent positive and put it under ane, ending upwardly with ${\displaystyle {\frac {1}{3^{2}}}}$ .^[6] Check out a few more than examples:

5. v

   Split up ii numbers with the same base of operations by subtracting the exponents. Division is the reverse of multiplication, and while they aren't always solved exactly contrary, they are hither. If you have the equation ${\displaystyle {\frac {4^{4}}{4^{2}}}}$ , simply subtract the acme exponent past the lesser and leave the base the same. Thus, ${\displaystyle {\frac {four^{4}}{4^{2}}}=four^{four-2}=4^{2}}$ , or xvi.

6. six

   Try out some practice problems to get use to manipulating exponential numbers. The post-obit problems cover everything currently shown. To see the respond, only highlight the unabridged line the problem is on.

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1. 1

2. 2

   Turn the pinnacle number into a normal exponent for mixed fractions. ${\displaystyle x^{\frac {v}{iii}}}$ might wait impossible, but it is like shooting fish in a barrel if yous remember how exponents are multiplied. Merely plow the base into a root, similar a normal fraction, so heighten the whole thing to the power on the height of the fraction. If you're struggling to remember this, think through the theory. For case:

3. 3

   Add, subtract, and multiply partial exponents just like normal. It is much easier to try and add together and subtract your exponents before solving them or turning them into roots. If the base of operations is the aforementioned and the exponent identical, you can add and subtract like normal. If the base is the aforementioned, yous can multiply and separate the exponents like normal as well, equally long equally your think how to add and decrease fractions. For example:

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• Question

  How do you solve fractional exponents?

  

  David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a individual tutoring visitor based in Los Angeles, California. With over 10 years of instruction feel, David works with students of all ages and grades in various subjects, also equally higher admissions counseling and test grooming for the SAT, ACT, ISEE, and more. Subsequently attaining a perfect 800 math score and a 690 English language score on the Saturday, David was awarded the Dickinson Scholarship from the Academy of Miami, where he graduated with a Bachelor'due south caste in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Large Ideas Math.

  

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• Question

  What practice you practise with negative exponents?

  

  David Jia is an Bookish Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of instruction experience, David works with students of all ages and grades in various subjects, likewise every bit college admissions counseling and test preparation for the SAT, Deed, ISEE, and more. Subsequently attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor's degree in Business Assistants. Additionally, David has worked as an teacher for online videos for textbook companies such equally Larson Texts, Big Ideas Learning, and Large Ideas Math.

  

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• Question

  How do y'all multiply exponents?

  

  David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring visitor based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well every bit higher admissions counseling and test grooming for the Sat, Act, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the Academy of Miami, where he graduated with a Bachelor's degree in Business organization Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

  

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  Adept Respond

  

  Support wikiHow by unlocking this expert answer.

  If you're multiplying exponents that have the same base of operations, add the exponents together. So if you have x^two times x^3, it becomes x^5. But if y'all're taking the exponent of a base of operations that already has an exponent, you multiply those exponents together. For example, if you're finding (x^2)^3, you'd multiply the 2 and the 3 to get ten^half-dozen.

• Question

  How do I solve 3^2/iii?

  

  Looking at the exponent two/3, the ii is a normal exponent (meaning you foursquare the base of operations number). The 3 is a root sign (meaning you find the cube root). In this case you would square three -- which is 9 -- and and so you notice the cube root of 9. If you wanted to, you could reverse the order of those ii operations by first finding the cube root of 3 and then squaring that number. In either instance the respond would be the aforementioned.

• Question

  How tin can I compute 4 to the power of 2 over three?

  

  Four to the power of 2 is 16, since 4 times 4 is sixteen. Then you lot split by iii, so xvi divided by 3 is 16/iii.

• Question

  Can someone delight explain how ii^3/2 equals two square root of two?

  

  I assume yous hateful 2^(3/two). Anything to the first power is itself and then two^1 is just ii. One-half exponents are square roots (Why? considering of the aforementioned rule): (ii^(1/2))*(two^(i/ii)) = two^(1/2+1/2) = 2^1 = ii ), so 2^(1/2) is the square root of 2. So the product simplifies to ii*sqrt(2).

• Question

  How tin I summate square root of 125 raised to the 6th power?

  

  √125 can be thought of equally 125 raised to the power of ½ (or 125^½). 125^½ raised to the sixth power is 125^3 = 1,953,125.

• Question

  Can you assistance me solve this problem? "What is the value of (x) in the following equation? X power 0.4 /16 = 32/10 ability 2.half-dozen?"

  

  (x^0.4)/xvi = 32/(x^2.vi). By cross multiplication, 10^3 =xvi*32 =2^(iv+5) [Exponents] =2^ix. So, ten = 2^3 =eight.

• Question

  How do I get rid of the exponent in (3a)^3?

  

  You cube root (3a)^3, then the exponent three can exist cancelled out by the cube root, and all you have at present is 3a.

• Question

  It's dealing with earthquakes. V is 10 times greater than four on the Richter scale. Uncomplicated x. ten. Simply how practise I solve when information technology's 5.5?

  

  The Richter scale is a log 10 scale. This ways that when you summate ratios, you summate them using your numbers in the exponents, and 10 is in the base of operations. For example, x^5/x^4 = 10. Then 10^5.v/10^iv = 31.62 - it's 31.62x stronger.

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• "Simplifying" in math ways do the indicated operations to go the simplest grade of the expressions involved.

• Most calculators have a push that you press to be the exponent after putting in the base of operations to solve exponent problems. It will probably be labeled as ^ or x^y.

• Base naught to the zero exponent, that is 0⁰ is non defined (sometimes called dne, does not exist). Computers or pocket calculators should render an error. Recall that whatsoever non-zero existent number to the power of 0 is ever ane, ${\displaystyle 4^{0}=i.}$

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• Increasing the exponents causes a product magnitude to rise very quickly, so that even if the answer may seem wrong, it may really be correct. (You lot tin check that past graphing any exponential function eastward.1000.: 2^x, if x has a range of values.)

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Article Summary X

To solve basic exponents, multiply the base number repeatedly for the number of factors represented by the exponent. If you need to add or subtract exponents, the numbers must take the same base and exponent. You can also multiply numbers with the aforementioned base past adding the exponents together and divide two numbers with the same base by subtracting the exponents! For tips on solving partial exponents, read on!

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