Solve 4x^-10y^30/5/frac{2y^20{x^20}}

$$\frac{ \frac{ 4 { x }^{ -10 } { y }^{ 30 } }{ 5 } }{ \frac{ 2 { y }^{ 20 } }{ { x }^{ 20 } } }$$

Evaluate

$$\frac{2\left(xy\right)^{10}}{5}$$

Solution Steps

Divide \frac{4x^{-10}y^{30}}{5} by \frac{2y^{20}}{x^{20}} by multiplying \frac{4x^{-10}y^{30}}{5} by the reciprocal of \frac{2y^{20}}{x^{20}}.

$$\frac{4x^{-10}y^{30}x^{20}}{5\times 2y^{20}}$$

Cancel out 2y^{20} in both numerator and denominator.

$$\frac{2x^{-10}y^{10}x^{20}}{5}$$

To multiply powers of the same base, add their exponents. Add -10 and 20 to get 10.

$$\frac{2x^{10}y^{10}}{5}$$

Differentiate w.r.t. x

$$4x^{9}y^{10}$$