How to Solve Exponents

Step-by-Step Guide

1. 1

   Step 1: Learn the correct words and vocab for exponent problems.

   When you have an exponent, like 23{\displaystyle 2^{3}}, you have two simple parts.
   
   The bottom number, here a 2, is the base.
   
   The number it is raised to, here a 3, is known as the exponent or power.
   
   If you are talking about 23{\displaystyle 2^{3}}, you would say it is "two to the third," "two to the third power," or "two raised to the third power." If a number is raised to the second power, like 52{\displaystyle 5^{2}}, you can also say that the number is squared, such as "five squared." If a number is raised to the third power, like 103{\displaystyle 10^{3}}, you can also say it is cubed, such as "ten cubed." If a number has no exponent shown, like a simple 4, it is technically to the first power and can be rewritten as 41{\displaystyle 4^{1}}.
   
   If the exponent is 0, and a "non-zero number" is raised to the "zero power"
   
   then the whole thing equals 1, such as 40=1{\displaystyle 4^{0}=1} or even something like (3/8)0=1.{\displaystyle (3/8)^{0}=1.}There is more about this in the "Tips" section.
2. 2

   Step 2: Multiply the base repeatedly for the number of factors represented by the exponent.

   If you need to solve an exponent by hand, start by rewriting it as a multiplication problem.
   
   You want to multiply the base by itself for the number of the exponent.
   
   So, if you have 34{\displaystyle 3^{4}} you would multiply three in a series of four separate factors, or 3∗3∗3∗3{\displaystyle 3*3*3*3}.
   
   More examples include: 45=4∗4∗4∗4∗4{\displaystyle 4^{5}=4*4*4*4*4} 82=8∗8{\displaystyle 8^{2}=8*8} Ten cubed =10∗10∗10{\displaystyle =10*10*10}, For example, with 45{\displaystyle 4^{5}}, you'd start with 4∗4∗4∗4∗4{\displaystyle 4*4*4*4*4} This looks daunting, but just take it one step at a time.
   
   Start by multiplying the first two fours.
   
   Then replace the two fours with the answer as shown here: 45=4∗4∗4∗4∗4{\displaystyle 4^{5}=4*4*4*4*4} 4∗4=16{\displaystyle 4*4=16} 45=16∗4∗4∗4{\displaystyle 4^{5}=16*4*4*4} , Keep multiplying in the numbers to "grow" your exponent.
   
   Continuing our example, you would multiple 16 by the next 4, so that: 45=16∗4∗4∗4{\displaystyle 4^{5}=16*4*4*4} 16∗4=64{\displaystyle 16*4=64} 45=64∗4∗4{\displaystyle 4^{5}=64*4*4} 64∗4=256{\displaystyle 64*4=256} 45=256∗4{\displaystyle 4^{5}=256*4} 256∗4=1024{\displaystyle 256*4=1024} As shown, you continue multiplying the base by your product of each first pair of numbers until you get your final answer.
   
   Simply keep multiplying the first two numbers, then multiply the answer by the next number in the sequence.
   
   This works for any exponent.
   
   Once you're done with our example, you should get 45=4∗4∗4∗4∗4=1024{\displaystyle 4^{5}=4*4*4*4*4=1024}. , 82{\displaystyle 8^{2}} 34{\displaystyle 3^{4}} 107{\displaystyle 10^{7}} , It is almost impossible to do larger exponents, like 915{\displaystyle 9^{15}} by hand, but calculators can handle it with ease.
   
   The button is usually clearly labeled.
   
   The Windows Seven calculator tool can be changed to scientific calculator mode by clicking the "View" tab of the calculator and selecting "Scientific".
   
   When you want the standard calculator mode back, use "View" and select "Standard".
   
   Google the expression to check your answer.
   
   You can use the "^" button on your computer, 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.
3. 3

   Step 3: Solve an expression: Multiply the first two numbers to get the product.

4. 4

   Step 4: Multiply that answer to your first pair (16 here) by the next number.

5. 5

   Step 5: Try your hand with a few more examples

6. 6

   Step 6: checking your answers with a calculator.

7. 7

   Step 7: Use the "exp

8. 8

   Step 8: " "xn{\displaystyle x^{n}}" or "^" button on a calculator to do exponents.

Detailed Guide

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