Question

Explain how to evaluate simplify and convert to radical form (x^3/8)^3/4

Answer 1

`(x^(3)/(8))^(3)/(4) = \sqrt[32]{x^9}`

Explanation:

Given

`(x^(3)/(8))^(3)/(4)`

Required

Convert to radical form

`(x^(3)/(8))^(3)/(4)`

Evaluate the exponents

`(x^(3)/(8))^(3)/(4) = x^(3*3)/(8*4)`

`(x^(3)/(8))^(3)/(4) = x^(9)/(32)`

Split the exponent

`(x^(3)/(8))^(3)/(4) = (x^9)^(1)/(32)`

Apply the following law of indices

`(x^a)^(1)/(b) = \sqrt[b]{x^a}`

So, we have:

`(x^(3)/(8))^(3)/(4) = \sqrt[32]{x^9}`