Solve (16x^4y^12)^frac{3{4}}

$$( 16 x ^ { 4 } y ^ { 12 } ) ^ { \frac { 3 } { 4 } }$$

Evaluate

$$8\left(|x|\right)^{3}\left(|y|\right)^{9}$$

Solution Steps

Expand \left(16x^{4}y^{12}\right)^{\frac{3}{4}}.

$$16^{\frac{3}{4}}\left(x^{4}\right)^{\frac{3}{4}}\left(y^{12}\right)^{\frac{3}{4}}$$

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

$$16^{\frac{3}{4}}x^{3}\left(y^{12}\right)^{\frac{3}{4}}$$

To raise a power to another power, multiply the exponents. Multiply 12 and \frac{3}{4} to get 9.

$$16^{\frac{3}{4}}x^{3}y^{9}$$

Calculate 16 to the power of \frac{3}{4} and get 8.

$$8x^{3}y^{9}$$

Differentiate w.r.t. x

$$24x|x|\left(|y|\right)^{9}$$