Solve sqrt[6]{16}

$$\sqrt[ 6 ] { 16 }$$

Evaluate

$$2^{\frac{2}{3}}\approx 1.587401052$$

Solution Steps

Rewrite 16 as 4^{2}.

$$\sqrt[6]{4^{2}}$$

Convert from radical to exponential form.

$$\left(4^{2}\right)^{\frac{1}{6}}$$

To raise a power to another power, multiply the exponents.

$$4^{\frac{2}{6}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Convert from exponential to radical form.

$$\sqrt[3]{4}$$