Solve {left({x}^frac{1{2}}{y}^-frac{2{3}}right)}^-frac{6{4}}

$${ \left( { x }^{ \frac{ 1 }{ 2 } } { y }^{ - \frac{ 2 }{ 3 } } \right) }^{ - \frac{ 6 }{ 4 } }$$

Evaluate

$$\frac{|y|}{x^{\frac{3}{4}}}$$

Solution Steps

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\left(x^{\frac{1}{2}}y^{-\frac{2}{3}}\right)^{-\frac{3}{2}}$$

Expand \left(x^{\frac{1}{2}}y^{-\frac{2}{3}}\right)^{-\frac{3}{2}}.

$$\left(x^{\frac{1}{2}}\right)^{-\frac{3}{2}}\left(y^{-\frac{2}{3}}\right)^{-\frac{3}{2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and -\frac{3}{2} to get -\frac{3}{4}.

$$x^{-\frac{3}{4}}\left(y^{-\frac{2}{3}}\right)^{-\frac{3}{2}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{2}{3} and -\frac{3}{2} to get 1.

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

Calculate y to the power of 1 and get y.

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

Differentiate w.r.t. x

$$-\frac{3|y|}{4x^{\frac{7}{4}}}$$