Question

Which expression shows the simplified form of (8 r Superscript negative 5 Baseline) Superscript negative 3? 8 r Superscript 15 StartFraction 8 Over r Superscript 15 Baseline EndFraction 512 r Superscript 15 StartFraction r Superscript 15 Baseline Over 512 EndFraction

Answer 1

D

Explanation:

Answer 2

`(r^(15))/(512)`

Explanation:

Given

`(8r^(-5))^(-3)`

Required

Simplify

This can be simplified using the following law of indices;

`(ab)^n = a^(n)b^(n)`

The equation becomes

`(8^(-3))(r^(-5))^(-3)`

Express
`8^(-3)` as a fraction

`((1)/(8^(3)))(r^(-5))^(-3)`

Simplify
`8^3`

`((1)/(8*8*8))(r^(-5))^(-3)`

`((1)/(512))(r^(-5))^(-3)`

The expression can further be simplified using the following law of indices;

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

`((1)/(512))(r^(-5))^(-3)` becomes

`((1)/(512))(r^(-5*-3))`

`((1)/(512))(r^(15))`

`(r^(15))/(512)`

Hence, the solution to
`(8r^(-5))^(-3)` is
`(r^(15))/(512)`