Question

What value of n makes the equation true? Show your work.

Answer 1

n = 6

Explanation:

`((-4)^(10))/((-4)^(n)) =(-4)^(2)*(-4)^(2)\\\\((-4)^(10))/((-4)^(n)) =(-4)^(2+2)\\\\((-4)^(10))/((-4)^(n)) =(-4)^(4)`

If they have the same base which is -4 we can either add or subtracting the exponent.

Add the exponenet when multiplying.

Subtract the exponent when dividing.

`(-4)^(10-n)=(-4)^4\\\\10-n=4\\10=4+n\\n= 6`

`((-4)^(10))/((-4)^(6))=(-4)^(10-6)=(-4)^4`

Answer 2

Answer:6

Explanation:

`(a^(b) )/(a^(c)) =a^(b-c) \\a^(b) *a^(c) =a^(b+c)\\ ((-4)^(10))/((-4)^(n))=(-4)^(2)*(-4)^(2) \\(-4)^(10-n)=(-4)^(4)\\ 10-n=4\\ -n=-6\\n=6`