Solve sqrt[192]{256}

$$\sqrt[ 192 ] { 256 }$$

Evaluate

$$\sqrt[24]{2}\approx 1.029302237$$

Solution Steps

Rewrite 256 as 2^{8}.

$$\sqrt[192]{2^{8}}$$

Convert from radical to exponential form.

$$\left(2^{8}\right)^{\frac{1}{192}}$$

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

$$2^{\frac{8}{192}}$$

Reduce the fraction \frac{8}{192} to lowest terms by extracting and canceling out 8.

$$2^{\frac{1}{24}}$$

Convert from exponential to radical form.

$$\sqrt[24]{2}$$