Question

$a^{\left(\frac{m}{n}\right)}$ can be written as:

• A. $\sqrt[m]{m\left(a^n\right)}$
• B. $\sqrt[n]{n\frac{1}{\left(a^m\right)}}$
• C. $\sqrt[n]{n\left(a^m\right)}$
• D. $\sqrt[n]{n\frac{1}{\left(a^m\right)}}$

Answer 1

The correct option is C

$\sqrt[n]{n\left(a^m\right)}$

$a^{\frac{m}{n}}$ = $a^{m\times \frac{1}{n}}$

$\because (x^a{)}^b=(x{)}^{a\times b}$

$\Rightarrow$ ${\left(a^m\right)}^{\left(\frac{1}{n}\right)}$

= $\sqrt[n]{n\left(a^m\right)}$