Question

Im cant figure out how to do this one ((-3)^2)^-3

Answer 1

`(1)/(729)`

Explanation:

`\left(\frac{}{}(-3)^2\frac{}{}\right)^(-3)`

First, we should evaluate inside the large parentheses:

`(-3)^2 = (-3)\cdot (-3) = 9`

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

`4^3 = 4 \, \cdot\, 4\, \cdot \,4`

↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where
`(-3)^2` was originally:

`(9)^(-3)`

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

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

Finally, we can apply this principle to the
`9^(-3)`:

`9^(-3) = (1)/(9^3) = \boxed{(1)/(729)}`