Solve (y^4*x^-frac{1{3}})^frac{3{4}}

$$( y ^ { 4 } \cdot x ^ { - \frac { 1 } { 3 } } ) ^ { \frac { 3 } { 4 } }$$

Evaluate

$$\left(\frac{y^{4}}{\sqrt[3]{x}}\right)^{\frac{3}{4}}$$

Solution Steps

Expand \left(y^{4}x^{-\frac{1}{3}}\right)^{\frac{3}{4}}.

$$\left(y^{4}\right)^{\frac{3}{4}}\left(x^{-\frac{1}{3}}\right)^{\frac{3}{4}}$$

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

$$y^{3}\left(x^{-\frac{1}{3}}\right)^{\frac{3}{4}}$$

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

$$y^{3}x^{-\frac{1}{4}}$$

Differentiate w.r.t. x

$$-\frac{y^{4}}{4|y|x^{\frac{5}{4}}}$$