Solve sqrt[8]{16}=

$$\sqrt[ 8 ] { 16 } =$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Rewrite 16 as 2^{4}.

$$\sqrt[8]{2^{4}}$$

Convert from radical to exponential form.

$$\left(2^{4}\right)^{\frac{1}{8}}$$

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

$$2^{\frac{4}{8}}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$2^{\frac{1}{2}}$$

Convert from exponential to radical form.

$$\sqrt{2}$$