Question

How do you simplify `(16x^12 )^(3/4)`?

Answer 1

Steps are given below

Explanation:

`(16x^12)^(3/4)`

First let us go through some rules.

`quad quad quad color(blue)((a*b)^m=a^m*b^m`
`quad quad quad color(blue)((a^m)^n=a^(mn)`

For example

`(2x^2)^3 = 2^3*(x^2)^3`

`quad quad quad quad quad=8x^(2*3)`

`quad quad quad quad quad=8x^6`

Also let us write `16` as `2^4`

Our problem

`(16x^12)^(3/4)` becomes

`quadcolor(green)((2^4x^12)^(3/4)`

`color(green)(=(2^4)^(3/4)*(x^12)^(3/4)`
`color(green)(=2^(4xx3/4)*x^(12xx3/4)`

`color(green)(=2^3*x^9`

`color(green)(=8*x^9quad` Answer