Question

Which is the simplified form of (9c^-9)^-3
b 1/729 c^27

Answer 1

Step-by-step explanation: the answer is b

Answer 2

`(9 {c}^( - 9) )^( - 3)=\frac{{c}^( 27) }{729}`

Step-by-step explanation

The given expression is

`(9 {c}^( - 9) )^( - 3)`

Recall that:

`({a}^(m) )^(n) = {a}^(mn)`

We use the law of exponents to get

`(9 {c}^( - 9) )^( - 3) = 9^( - 3) {c}^( - 9 * - 3)`

Let us multiply in the exponents to get:

`(9 {c}^( - 9) )^( - 3) = 9^( - 3) {c}^( 27)`

Recall again that:

`{a}^( - m) = \frac{1}{ {a}^(m) }`

This implies that:

`(9 {c}^( - 9) )^( - 3) = \frac{1}{ {9}^( 3) } * {c}^( 27)`

We expand the power to get:

`(9 {c}^( - 9) )^( - 3) = (1)/(9 * 9 * 9) * {c}^( 27)`

`(9 {c}^( - 9) )^( - 3)=(1)/(729) * {c}^( 27)`

We multiply out to get:

`(9 {c}^( - 9) )^( - 3)=\frac{{c}^( 27) }{729}`