Question

What is the value of the expression

(−3^2/3^3)2
when it is simplified?
Enter your answer as the correct value.

Answer 1

So either you meant
`((-3^2)/(-3^3) )*(2)/(1)`, or you actually meant
`((-3^2)/(-3^3) )^2` . I'll solve both.

`((-3^2)/(-3^3) )*(2)/(1)`

Firstly, do the division. Since the numerator and the denominator have the same base, you can write it as -3^-1, which can be rewritten as -1/3.
`-(1)/(3)*(2)/(1)`

Next, multiply the fractions, and your answer should be
`-(2)/(3)`

`((-3^2)/(-3^3) )^2`

Firstly, multiply square with the powers in the fraction to get
`(-3^4)/(-3^6)`

Next, divide. Like before, they have the same base, so the answer can be written as -3^-2, which can be rewritten as 1/3^2 = 1/9.

Answer 2

`(-(3^2)/(3^3) )^2 = (-(1)/(3) )^2 = (1)/(9)`

OR (in more details):

`(-(3^2)/(3^3) )^2 = (-3^(2-3))^2 = (-3^(-1))^2 = (-(1)/(3) )^2 = (1)/(9)`