Question

How do you simplify ${16}^{\frac{3}{4}}$?

Answer 1

Simplify the given number:

The given irrational number is ${16}^{\frac{3}{4}}$.

$\therefore {16}^{\frac{3}{4}}={\left(2\times 2\times 2\times 2\right)}^{\frac{3}{4}}$

$={\left(2^4\right)}^{\frac{3}{4}}$

$=2^3$ $\mathbf{.}\mathbf{.}\mathbf{.}\left[\because {\left(a^m\right)}^n=a^{mn}\right]$

$=8$

Hence, the simplified value of ${16}^{\frac{3}{4}}$ is $8$.