Solve (x^frac{1{2}}y^frac{2{3}})^6

$$( x ^ { \frac { 1 } { 2 } } y ^ { \frac { 2 } { 3 } } ) ^ { 6 }$$

Evaluate

$$x^{3}y^{4}$$

Solution Steps

Expand \left(x^{\frac{1}{2}}y^{\frac{2}{3}}\right)^{6}.

$$\left(x^{\frac{1}{2}}\right)^{6}\left(y^{\frac{2}{3}}\right)^{6}$$

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

$$x^{3}\left(y^{\frac{2}{3}}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 6 to get 4.

$$x^{3}y^{4}$$

Expand

$$x^{3}y^{4}$$

Solution Steps

Expand \left(x^{\frac{1}{2}}y^{\frac{2}{3}}\right)^{6}.

$$\left(x^{\frac{1}{2}}\right)^{6}\left(y^{\frac{2}{3}}\right)^{6}$$

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

$$x^{3}\left(y^{\frac{2}{3}}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 6 to get 4.

$$x^{3}y^{4}$$