Solve (x^-5y^1/3)^-3/5=

$$( x ^ { - 5 } y ^ { 1 / 3 } ) ^ { - 3 / 5 } =$$

Evaluate

$$\frac{x^{3}}{\sqrt[5]{y}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(x^{-5}\sqrt[3]{y}\right)^{-\frac{3}{5}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(x^{-5}\right)^{-\frac{3}{5}}\left(\sqrt[3]{y}\right)^{-\frac{3}{5}}$$

To raise a power to another power, multiply the exponents.

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

Multiply -5 times -\frac{3}{5}.

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

Multiply \frac{1}{3} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x^{3}\times \frac{1}{\sqrt[5]{y}}$$

Differentiate w.r.t. x

$$\frac{3x^{2}}{\sqrt[5]{y}}$$