How to Figure out 10 to the Power of Any Positive Integer

Last Updated: January 25, 2022 References

Figuring out 10 to the power of any positive integer^{[1]
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Research source} 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.^{[2]
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Research source} 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.^{[3]
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2
Subtract 1 from the value of the exponent. In this case, 2-1 = 1, so you're left with 1.

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3
Write this many zeroes after "10" and you're all done. You can also just think of 10^x 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.^{[4]
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Research source} 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.^{[5]
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Research source} 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.

Community Q&A

Question

What is the solution for 10 x 10 to the -10?

Community Answer

10 is the same as 10 to the power of +1. To determine the resultant power of the multiplication, simply add the powers of 10. You get 1+(-10) = -9. The answer is 10 to power of -9, or 0.000000001.
Question

How do I calculate 10 to the power of 30 divided by 10 to the power of 24?

Donagan

Top Answerer

Simply subtract the second exponent from the first to get the answer, 10^6.
Question

What is 10 to the power of 1.08?

LyKaxandra Caimoy

Community Answer

First, convert it to a fraction. The denominator becomes the root for the √ and the numerator is the exponent. For example, 10^(27/25) 25√10^27.