Answer :
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.
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.
