Solve (2x^frac{2{3}})^4

$$( 2 x ^ { \frac { 2 } { 3 } } ) ^ { 4 }$$

Evaluate

$$16x^{\frac{8}{3}}$$

Solution Steps

Expand \left(2x^{\frac{2}{3}}\right)^{4}.

$$2^{4}\left(x^{\frac{2}{3}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 4 to get \frac{8}{3}.

$$2^{4}x^{\frac{8}{3}}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{\frac{8}{3}}$$

Expand

$$16x^{\frac{8}{3}}$$

Solution Steps

Expand \left(2x^{\frac{2}{3}}\right)^{4}.

$$2^{4}\left(x^{\frac{2}{3}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 4 to get \frac{8}{3}.

$$2^{4}x^{\frac{8}{3}}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{\frac{8}{3}}$$