Question

If a, m, n are positive integers, then ${\left\{\sqrt[m]{m\sqrt[n]{na}}\right\}}^{mn}$ is equal to

• A. $a^{mn}$
• B. a
• C. $a^{\frac{m}{n}}$
• D. 1

Answer 1

The correct option is B

a

${\left\{\sqrt[m]{m\sqrt[n]{na}}\right\}}^{mn}={\left[{\left(a^{\frac{1}{n}}\right)}^{\frac{1}{m}}\right]}^{mn}={\left(a^{\frac{1}{mn}}\right)}^{mn}=a^{\frac{mn}{mn}}=a$