Question

Need help onna problem do you mind help me please

Answer 1

Given the expresssion;

$(\sqrt[5]{x^7})^3$

First, we start with the expression in the bracket which is;

$\sqrt[5]{x^7}$

We apply the fractional exponent rule of indices which is;

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

Applying the law to the expression in the bracket above, we have;

$\begin{gathered} \sqrt[5]{x^7}=(x^7)^{\frac{1}{5}} \\ \sqrt[5]{x^7}=x^{\frac{7}{5}} \end{gathered}$

Thus, the given expression is;

$(\sqrt[5]{x^7})^3=(x^{\frac{7}{5}})^3$

Then, we multiply the exponents, we have;

$(\sqrt[5]{x^7})^3=x^{\frac{21}{5}}$