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Exponents review

Review the basics of exponents and try some practice problems. 

Exponents and bases

Here's what an exponent and a base look like:
43
The small number written above and to the right of a number is called an exponent. The number underneath the exponent is called the base. In this example, the base is 4, and the exponent is 3.
Want to learn more about exponents? Check out this video.

Evaluating exponents

An exponent tells us to multiply the base by itself that number of times.
In our example, 43 tells us to multiply the base of 4 by itself 3 times:
43=4×4×443=64

What about when the exponent is a zero?

Any base with an exponent of zero is equal to 1.
For example, 70=1.
Check out this video to see why.

Practice

Problem 1
Evaluate.
92=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Want to try more problems like this? Check out this exercise.

Want to join the conversation?

  • blobby green style avatar for user cpime-s049
    why is 5 to the 0 power 1?
    (139 votes)
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    • female robot grace style avatar for user preeti
      Good question! Look at the following exponents:
      2^4 = 16
      2^3 = 8
      2^2 = 4
      2^1 = 2
      2^0 = __
      Respective to the pattern, what comes next?! 1!

      Take a look at this:
      2^(m-n) = 2^m/2^n
      If m = n...
      2^(1-1) = 2^1/2^1
      2^0 = 1

      Hope this helps!
      (198 votes)
  • duskpin sapling style avatar for user Trinity Thorn
    i get confused and multiply ex. 5 x 2 =10 when its 25 how can i rember to times it by 2 also how is 5 times 0 equal to 1? ':(
    (33 votes)
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    • starky ultimate style avatar for user Hector Soto
      So for exponents you need to think about it a bit different. I will use the example you gave of 5 raised to the 2nd exponent (5^2) for my explanation. The exponent (the number 2) is the number of bases (the number 5) you multiply together. So for 5^2, you would use two 5's and multiply them together which is simply 5x5=25. So for another example if we lower the exponent to 1, we would be looking at 5^1. Well let's apply the same principle of using just one 5, which is simply 5=5.

      Let's move on to your second question which is a touch more complicated. I will simplify it for you though. Once your exponent is less than 1 the rules get a little different and you start dealing with fractions. 5^0 = 5*(1/5) = 1. The exponent in this case is the number + 1 that you divide the base number by. I illustrated it with multiplying it by a fraction, but the principle is still the same. I know this can be a difficult topic to understand at first, and explanation isn't the exact proof/theorem, but I do hope it helps you get a basic understanding of exponents.
      (64 votes)
  • duskpin ultimate style avatar for user Ash
    I'm going into sixth grade.
    is it ok for me to do eight-grade stuff?
    Or should I still just do sixth?
    (22 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      It really depends on your level of math skill.

      If you’re an advanced math student with a strong understanding of arithmetic operations with whole numbers, fractions, decimals, and integers, then yes you can try 8th grade math. Keep in mind that you will frequently encounter variables (letters that represent unknown numbers) in 8th grade math.

      On the other hand, if you tend to have difficulty with math, then doing 6th grade math would be the better choice.

      Have a blessed, wonderful day!
      (26 votes)
  • mr pants purple style avatar for user 25MHAAR
    how does 5 with the exponent of 0 have the answer of 1.
    (18 votes)
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    • sneak peak yellow style avatar for user William Wang
      Well, I think that CycoCyco answered it somewhat well, but here's another explanation from me:

      When having an exponent (such as 5 to the power of 2), you're setting up 5^2, or 5 * 5, which equals one. Same with having five raised to the power of one, which equals five.

      In earlier grades, you leaned that 5 * 0 = 0. But in math, 5^0 = 1, because you're not raising the power by anything.

      I hope this explanation helped.
      (26 votes)
  • aqualine sapling style avatar for user Hannah
    What about negative exponents? How do you figure those out?
    (14 votes)
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  • piceratops seedling style avatar for user ♥ [っ◔◡◔]っ ♥
    I dont understand why 5'0 pwr is = to 1
    (16 votes)
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  • blobby green style avatar for user Elle B.
    Idk why the power of 0 is always 1 but it makes it easier for me.
    (12 votes)
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  • female robot ada style avatar for user 30ktran16
    I don’t get 5 to the power 0
    (10 votes)
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    • hopper cool style avatar for user Philip
      Any positive value to the power of 0 equals 1. The reason is that, since exponents represent repeated multiplication, then applying the power of 0 is essentially dividing a value by itself the specific number of times. For example, if we have 5^0, then that means we are multiplying it by its reciprocal the specific number of times it got multiplied. So when we have 5^0, are multiplying 5 by itself a specific number of times, then dividing by 5 the same exact number of times it got multiplied. Therefore, every single time a 5 was multiplied, it will be removed by division through the reciprocal, ending up with a 1.
      (13 votes)
  • aqualine ultimate style avatar for user RAVENCLAWGAMER24
    how is 5 to the 0 power not 0 because 5 zero times is 0
    (7 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      In general, x to the y power is usually not x times y. So it is a mistake to assume that 5 to the 0 power is 5 times 0.

      Look at the following pattern:

      5^4 = 5 * 5 * 5 * 5
      5^3 = 5 * 5 * 5 = (5 * 5 * 5 * 5)/5
      5^2 = 5 * 5 = (5 * 5 * 5)/5
      5^1 = 5 = (5 * 5)/5

      As we can see, each time the exponent goes down by 1, the answer is divided by 5. Continuing the pattern gives 5^0 = 5/5 = 1.

      Have a blessed, wonderful day!
      (18 votes)
  • male robot johnny style avatar for user Kaleb Amar
    I keep on getting confused with the base and the exponent. Can someone help?
    (9 votes)
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    • aqualine ultimate style avatar for user Zen
      The base is the number below for example in 5^2, 5 is the base and 2 is the exponent. Which means that this would expand to 5 x 5 = 25. The exponent tells you how many times the base will be multiplied by itself, we knew that the 5 would be multiplied by itself twice because the exponent was 2.
      (10 votes)