Question

Evaluate :
(a) $\sqrt[8]{8\frac{6561}{65536}}$ (b) ${\left(15625\right)}^{\frac{1}{6}}$.

Answer 1

We have,

$\left(a\right)$ $\sqrt[8]{8\frac{6561}{65536}}$

$=\sqrt[8]{8\frac{3^8}{4^8}}={\left(\frac{3}{4}\right)}^{\frac{1}{8}\times 8}$

$=\frac{3}{4}$ $=0.75$.

$\left(b\right)$ ${\left(15625\right)}^{1/6}=5^{6\times \frac{1}{6}}=5$.