Solve (16x^14y^-18)^frac{5{2}}

$$( 16 x ^ { 14 } y ^ { - 18 } ) ^ { \frac { 5 } { 2 } }$$

Evaluate

$$\frac{1024\left(|x|\right)^{35}}{\left(|y|\right)^{45}}$$

Solution Steps

Expand \left(16x^{14}y^{-18}\right)^{\frac{5}{2}}.

$$16^{\frac{5}{2}}\left(x^{14}\right)^{\frac{5}{2}}\left(y^{-18}\right)^{\frac{5}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 14 and \frac{5}{2} to get 35.

$$16^{\frac{5}{2}}x^{35}\left(y^{-18}\right)^{\frac{5}{2}}$$

To raise a power to another power, multiply the exponents. Multiply -18 and \frac{5}{2} to get -45.

$$16^{\frac{5}{2}}x^{35}y^{-45}$$

Calculate 16 to the power of \frac{5}{2} and get 1024.

$$1024x^{35}y^{-45}$$

Differentiate w.r.t. x

$$\frac{35840|x|x^{33}}{\left(|y|\right)^{45}}$$