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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:
start color #11accd, 4, end color #11accd, start superscript, start color #e07d10, 3, end color #e07d10, end superscript
The small number written above and to the right of a number is called an start color #e07d10, start text, e, x, p, o, n, e, n, t, end text, end color #e07d10. The number underneath the exponent is called the start color #11accd, start text, b, a, s, e, end text, end color #11accd. In this example, the base is start color #11accd, 4, end color #11accd, and the exponent is start color #e07d10, 3, end color #e07d10.
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, start color #11accd, 4, end color #11accd, start superscript, start color #e07d10, 3, end color #e07d10, end superscript tells us to multiply the base of start color #11accd, 4, end color #11accd by itself start color #e07d10, 3, end color #e07d10 times:
43=4×4×443=64\begin{aligned} \blueD4^\goldD3 &=\blueD4 \times \blueD4 \times \blueD4 \\\\ \phantom{\blueD4^\goldD3}&= 64 \end{aligned}

What about when the exponent is a zero?

Any base with an exponent of zero is equal to 1.
For example, 7, start superscript, 0, end superscript, equals, 1.
Check out this video to see why.

Practice

Problem 1
  • Current
Evaluate.
9, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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?
    (102 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!
      (127 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? ':(
    (24 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.
      (45 votes)
  • mr pants purple style avatar for user 25MHAAR
    how does 5 with the exponent of 0 have the answer of 1.
    (14 votes)
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    • stelly green style avatar for user King
      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.
      (16 votes)
  • aqualine sapling style avatar for user Hannah
    What about negative exponents? How do you figure those out?
    (9 votes)
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  • piceratops seedling style avatar for user ♥ [っ◔◡◔]っ ♥
    I dont understand why 5'0 pwr is = to 1
    (12 votes)
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  • aqualine ultimate style avatar for user AIDENT
    why do i like men
    (9 votes)
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  • male robot johnny style avatar for user Kaleb Amar
    I keep on getting confused with the base and the exponent. Can someone help?
    (6 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.
      (5 votes)
  • starky seed style avatar for user auskin
    how is 5 to the 0 power not 0 because 5 zero times is 0
    (3 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!
      (11 votes)
  • blobby green style avatar for user Jennifer Andreucci-Young
    Hey how to I remember bases vs exponents?
    (2 votes)
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    • leaf blue style avatar for user Bri
      I remember Bases because they are on the bottom of the number just like the bottom of the triangle is called the base. Exponents... let's take a 5k race, for example, John is in the lead which would show him at the top of the leader board which would make us think he is an expert racer... EX-ponent- EX-pert. Hope this helps Jennifer!
      (10 votes)
  • blobby blue style avatar for user bascoari000
    how do you add or multiply exponents together without getting rid of the exponents? for example if you had -2x^4+4x^2+5 -7x^5 would you add all the exponents together or would you leave them by their selves?
    (5 votes)
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    • stelly blue style avatar for user Kim Seidel
      You have 4 unlike terms. You can't combine any of them.
      Remember, exponents represent repetitive multiplication of a common base. You only change an exponent if you are multiplying or dividing a common base. In your expression, the operation is addition/subtraction. So, the exponents can't be changed.
      Hope this helps.
      (2 votes)