Question

Describe the process of rewriting the expression Please Help

Answer 1

Answer:

$x^{\frac{21}{4} }$

Step-by-step explanation:

Given expression is:

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

First we will use the rule:

$\sqrt[n]{x} = x^{\frac{1}{n} }$

So for the given expression:

$\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }$

We will use tha property of multiplication on powers:

$=x^{7*\frac{1}{8} }$

$= x^{\frac{7}{8} }$

Applying the outer exponent now

$(x^{\frac{7}{8} })^6$

$= x^{\frac{7}{8}*6 } \\= x^{\frac{42}{8} }\\= x^{\frac{21}{4} }$