Question

Which expression is equivalent to(r^-7)^6?

Answer 1

(r^-7)^6 = r^-42 . . . . exponents are multiplied

Answer 2

`(1)/(r^(42))` is equivalent to
`(r^(-7))^6`

Explanation:

Using the exponent rule:

`(a^n)^m = a^(nm)`

`a^(-n) = (1)/(a^n)`

Given the radical expression:

`(r^(-7))^6`

Apply the rule we have;

`r^(-7 \cdot 6)`

Simplify:

`r^(-42)`

Again, apply the rule:

`(1)/(r^(42))`

Therefore, the expression is equivalent to
`(r^(-7))^6`

`(1)/(r^(42))`.