Solve (x^3/y^7)^-1

$$( \frac { x ^ { 3 } } { y ^ { 7 } } ) ^ { - 1 }$$

Evaluate

$$\frac{y^{7}}{x^{3}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

$$\frac{1}{\frac{x^{3}}{y^{7}}}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{1}{x^{3}\times \frac{1}{y^{7}}}$$

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

$$\frac{x^{3\left(-1\right)}}{y^{7\left(-1\right)}}$$

Multiply 3 times -1.

$$\frac{x^{-3}}{y^{7\left(-1\right)}}$$

Multiply 7 times -1.

$$\frac{1}{x^{3}y^{-7}}$$

Differentiate w.r.t. x

$$-\frac{3y^{7}}{x^{4}}$$