Solve sqrt[14]{128}

$$\sqrt[ 14 ] { 128 }$$

Evaluate

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

Solution Steps

Rewrite 128 as 2^{7}.

$$\sqrt[14]{2^{7}}$$

Convert from radical to exponential form.

$$\left(2^{7}\right)^{\frac{1}{14}}$$

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

$$2^{\frac{7}{14}}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

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

Convert from exponential to radical form.

$$\sqrt{2}$$