Solve (y^-3z)^frac{3{4}}

$$( y ^ { - 3 } z ) ^ { \frac { 3 } { 4 } }$$

Evaluate

$$\left(\frac{z}{y^{3}}\right)^{\frac{3}{4}}$$

Solution Steps

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

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

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

$$y^{-\frac{9}{4}}z^{\frac{3}{4}}$$

Differentiate w.r.t. y

$$-\frac{9z}{4\sqrt[4]{zy^{13}}}$$