Solve (x^-6/9y^-4)^-frac{1{2}}

$$( \frac { x ^ { - 6 } } { 9 y ^ { - 4 } } ) ^ { - \frac { 1 } { 2 } }$$

Evaluate

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

Solution Steps

To raise \frac{x^{-6}}{9y^{-4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{-6}\right)^{-\frac{1}{2}}}{\left(9y^{-4}\right)^{-\frac{1}{2}}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -\frac{1}{2} to get 3.

$$\frac{x^{3}}{\left(9y^{-4}\right)^{-\frac{1}{2}}}$$

Expand \left(9y^{-4}\right)^{-\frac{1}{2}}.

$$\frac{x^{3}}{9^{-\frac{1}{2}}\left(y^{-4}\right)^{-\frac{1}{2}}}$$

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

$$\frac{x^{3}}{9^{-\frac{1}{2}}y^{2}}$$

Calculate 9 to the power of -\frac{1}{2} and get \frac{1}{3}.

$$\frac{x^{3}}{\frac{1}{3}y^{2}}$$

Differentiate w.r.t. x

$$\frac{9x|x|}{y^{2}}$$