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

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.

Answered by Samilina | 2024-06-10

The number that meets the conditions of the equation is 5. We simplified the expression using exponent rules and found the cube root of 125. Verification confirms that this solution is correct.
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Answered by Samilina | 2024-10-14