Answer:
[tex]x^{\frac{21}{4} }[/tex]
Step-by-step explanation:
Given expression is:
[tex](\sqrt[8]{x^7} )^{6}[/tex]
First we will use the rule:
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
So for the given expression:
[tex]\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }[/tex]
We will use tha property of multiplication on powers:
[tex]=x^{7*\frac{1}{8} }[/tex]
[tex]= x^{\frac{7}{8} }[/tex]
Applying the outer exponent now
[tex](x^{\frac{7}{8} })^6[/tex]
[tex]= x^{\frac{7}{8}*6 } \\= x^{\frac{42}{8} }\\= x^{\frac{21}{4} }[/tex]
