Solve sqrt[9]{27}

$$\sqrt[ 9 ] { 27 }$$

Evaluate

$$\sqrt[3]{3}\approx 1.44224957$$

Solution Steps

Rewrite 27 as 3^{3}.

$$\sqrt[9]{3^{3}}$$

Convert from radical to exponential form.

$$\left(3^{3}\right)^{\frac{1}{9}}$$

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

$$3^{\frac{3}{9}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

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

Convert from exponential to radical form.

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