Solve -3(16xy^8)^frac{3{4}}

$$- 3 ( 16 x y ^ { 8 } ) ^ { \frac { 3 } { 4 } }$$

Evaluate

$$-24\left(xy^{8}\right)^{\frac{3}{4}}$$

Solution Steps

Expand \left(16xy^{8}\right)^{\frac{3}{4}}.

$$-3\times 16^{\frac{3}{4}}x^{\frac{3}{4}}\left(y^{8}\right)^{\frac{3}{4}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and \frac{3}{4} to get 6.

$$-3\times 16^{\frac{3}{4}}x^{\frac{3}{4}}y^{6}$$

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

$$-3\times 8x^{\frac{3}{4}}y^{6}$$

Multiply -3 and 8 to get -24.

$$-24x^{\frac{3}{4}}y^{6}$$

Differentiate w.r.t. x

$$-\frac{18y^{6}}{\sqrt[4]{x}}$$