Solve (5x^{2}y^{3})^0div(-2x^-3y^5)^-2

$$( 5 x ^ { 2 } y ^ { 3 } ) ^ { 0 } \div ( - 2 x ^ { - 3 } y ^ { 5 } ) ^ { - 2 }$$

Evaluate

$$\frac{4y^{10}}{x^{6}}$$

Solution Steps

Calculate 5x^{2}y^{3} to the power of 0 and get 1.

$$\frac{1}{\left(-2x^{-3}y^{5}\right)^{-2}}$$

Expand \left(-2x^{-3}y^{5}\right)^{-2}.

$$\frac{1}{\left(-2\right)^{-2}\left(x^{-3}\right)^{-2}\left(y^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -2 to get 6.

$$\frac{1}{\left(-2\right)^{-2}x^{6}\left(y^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{1}{\left(-2\right)^{-2}x^{6}y^{-10}}$$

Calculate -2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{\frac{1}{4}x^{6}y^{-10}}$$

Differentiate w.r.t. x

$$-\frac{24y^{10}}{x^{7}}$$