Question

Find the value of ${\left(16\right)}^{\frac{3}{4}}$

Answer 1

Solve for the required value

Given ${\left(16\right)}^{\frac{3}{4}}$

We know that ,$16=2^4$

$$\begin{gathered} \therefore {\left(16\right)}^{\frac{3}{4}}={\left(2^4\right)}^{\frac{3}{4}} \\ ={\left(2\right)}^{4\times \frac{3}{4}}\left[\because {\left(a^m\right)}^n=a^{m\times n}\right] \\ =2^3 \\ \Rightarrow {\left(16\right)}^{\frac{3}{4}}=8 \end{gathered}$$

Hence, the value of ${\left(16\right)}^{\frac{3}{4}}$ is $8$