Solve (r^1/6s^1/6)^2

$$( r ^ { 1 / 6 } s ^ { 1 / 6 } ) ^ { 2 }$$

Evaluate

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

Solution Steps

Expand \left(r^{\frac{1}{6}}s^{\frac{1}{6}}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply \frac{1}{6} and 2 to get \frac{1}{3}.

$$r^{\frac{1}{3}}\left(s^{\frac{1}{6}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{6} and 2 to get \frac{1}{3}.

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

Expand

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

Solution Steps

Expand \left(r^{\frac{1}{6}}s^{\frac{1}{6}}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply \frac{1}{6} and 2 to get \frac{1}{3}.

$$r^{\frac{1}{3}}\left(s^{\frac{1}{6}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{6} and 2 to get \frac{1}{3}.

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