Question

Describe the process of rewriting the expression Please Help

Answer 1

`x^{(21)/(4) }`

Explanation:

Given expression is:

`(\sqrt[8]{x^7} )^(6)`

First we will use the rule:

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

So for the given expression:

`\sqrt[8]{x^(7)}=(x^(7) )^{(1)/(8) }`

We will use tha property of multiplication on powers:

`=x^{7*(1)/(8) }`

`= x^{(7)/(8) }`

Applying the outer exponent now

`(x^{(7)/(8) })^6`

`= x^{(7)/(8)*6 } \\= x^{(42)/(8) }\\= x^{(21)/(4) }`