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^{(m)/(n)}=(x^m)^{(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)^{(1)/(5)} \\ \sqrt[5]{x^7}=x^{(7)/(5)} \end{gathered}`

Thus, the given expression is;

`(\sqrt[5]{x^7})^3=(x^{(7)/(5)})^3`

Then, we multiply the exponents, we have;

`(\sqrt[5]{x^7})^3=x^{(21)/(5)}`