# What is the simplified expression of ³(the square root of)64⁶ ?

Jun 20, 2018

${64}^{2} = 4096$

#### Explanation:

This question becomes easy if you remember that extracting the $n$-th root is the same as raising to the $\frac{1}{n}$-th power.

So, $\setminus \sqrt[3]{{64}^{6}} = {\left({64}^{6}\right)}^{\frac{1}{3}}$

Now use the formula ${\left({a}^{b}\right)}^{c} = {a}^{b c}$ to get

${64}^{6 \cdot \frac{1}{3}} = {64}^{2}$

In case you need it, ${64}^{2} = 4096$