Figure out 10 to the Power of Any Positive Integer

Figuring out 10 to the power of any positive integer is easier than it looks. All you have to do is know that the exponent above the number 10 simply indicates the number of times that you have to multiply 10 by itself. Once you master this concept, you'll be on your way to being an exponent expert.

Steps

  1. Find the value of the exponent. Let's say that you're working with trying to find 102. In this case, the positive integer you're working with is 2.[1]
  2. Subtract 1 from the value of the exponent. In this case, 2-1 = 1, so you're left with 1.
  3. Write this many zeroes after "10" and you're all done. You can also just think of 10x to simply be equal to the number 1 followed by x zeroes.
    • In this case, you can see that 102 = 100. This is because you've found the exponent, 2, subtracted 1 from it to get 1, and then added just 1 0 after "10" to get 100, your answer.
  4. Understand that the exponent is the amount of times that you multiply 10 by itself. To have a better understanding of how to figure out 10 to the power of any positive integer, or even to take a shortcut, all you have to know is that the exponent just shows the amount of times you'll have to multiply 10 by itself. You can also do this to find your answer.
    • For example: 103 = 1000 because 10 x 10 x 10 = 1000.
    • 104 = 10 x 10 x 10 x 10 or 10,000.
    • 105 = 10 x 10 x 10 x 10 x 10 = 100,000.
    • 106 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000
    • 107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000
  5. Know that any number to the power of 0 is 1. Though 0 is neither positive or negative, this can be an important rule to learn as you become more knowledgeable about exponents. This is as true for 100 as it is for 5,3560.
    • Therefore, 100 = 1, 50 = 1, 210 = 1, and so on.
    • You can also think of it this way: 10 to the power of 0 is 1 because 0 is the amount of zeros that go after 1 and if zero zeros are after 1, that makes the answer 1.

Things You'll Need

  • Computer to research these techniques (optional)
  • Math textbook (optional)
  • Calculator (optional)

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Sources and Citations

  1. ↑ http://www.purplemath.com/modules/exponent.htm

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