# What is 64^(1/3) ?

Jul 26, 2017

${64}^{\frac{1}{3}} = 4$

#### Explanation:

${64}^{\frac{1}{3}} = \sqrt[3]{64}$

When finding roots of integers it is often helpful to express the integer as its prime factors.

$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

$\therefore \sqrt[3]{64} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2}$

We can now take each triple through the root one time.

$\therefore \sqrt[3]{64} = 2 \times 2 = 4$

Hence, ${64}^{\frac{1}{3}} = 4$

Jul 26, 2017

$4$

#### Explanation:

${64}^{\frac{1}{3}}$

$= {\left(4 \times 4 \times 4\right)}^{\frac{1}{3}}$

$= {4}^{\left(3 \times \frac{1}{3}\right)}$

$= {4}^{1}$

$= 4$