Solve (x^frac{1{2}}y^frac{1{4}}z^frac{1{4}})^12

$$( x ^ { \frac { 1 } { 2 } } y ^ { \frac { 1 } { 4 } } z ^ { \frac { 1 } { 4 } } ) ^ { 12 }$$

Evaluate

$$x^{6}\left(yz\right)^{3}$$

Solution Steps

Expand \left(x^{\frac{1}{2}}y^{\frac{1}{4}}z^{\frac{1}{4}}\right)^{12}.

$$\left(x^{\frac{1}{2}}\right)^{12}\left(y^{\frac{1}{4}}\right)^{12}\left(z^{\frac{1}{4}}\right)^{12}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 12 to get 6.

$$x^{6}\left(y^{\frac{1}{4}}\right)^{12}\left(z^{\frac{1}{4}}\right)^{12}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{4} and 12 to get 3.

$$x^{6}y^{3}\left(z^{\frac{1}{4}}\right)^{12}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{4} and 12 to get 3.

$$x^{6}y^{3}z^{3}$$

Expand

$$x^{6}\left(yz\right)^{3}$$

Solution Steps

Expand \left(x^{\frac{1}{2}}y^{\frac{1}{4}}z^{\frac{1}{4}}\right)^{12}.

$$\left(x^{\frac{1}{2}}\right)^{12}\left(y^{\frac{1}{4}}\right)^{12}\left(z^{\frac{1}{4}}\right)^{12}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 12 to get 6.

$$x^{6}\left(y^{\frac{1}{4}}\right)^{12}\left(z^{\frac{1}{4}}\right)^{12}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{4} and 12 to get 3.

$$x^{6}y^{3}\left(z^{\frac{1}{4}}\right)^{12}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{4} and 12 to get 3.

$$x^{6}y^{3}z^{3}$$