A number to the 12th power divided by the same number to the 9th power equals 125.what is the number

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22-09-2014
Mathematics

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A number to the 12th power divided by the same number to the 9th power equals 125.what is the number

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Samilina Samilina · Answer 1 · 2014-09-22T21:00:55-04:00

n^12/n^9 = 125
Let's use our product rules first!
n*n*n*n*n*n*n*n*n*n*n*n/n*n*n*n*n*n*n*n*n

We can cancel out nine of those and we're left with:
n^3 = 125.

We should expand that....
n*n*n = 125.

What times itself three times is 125? Oh! That would be the cubed root! Let's find it.
4*4*4 = 64, so that's not it.
How about 6*6*6? Nope, that's 216.
Hmm... 5*5*5? Yes! That's it.

That means we're left with n=5. Let's plug it back in, just to check.
5^12/5^9 = 125
5^3 = 125
5*5*5 = 125

That's correct, so your answer would be that the number is 5.