Solve (3x^2y^-4)^-1

$$( 3 x ^ { 2 } y ^ { - 4 } ) ^ { - 1 }$$

Evaluate

$$\frac{y^{4}}{3x^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\frac{1}{3x^{2}y^{-4}}$$

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

$$\frac{1}{3}\times \frac{1}{x^{2}}\times \frac{1}{y^{-4}}$$

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

$$\frac{1}{3}x^{2\left(-1\right)}y^{-4\left(-1\right)}$$

Multiply 2 times -1.

$$\frac{1}{3}\times \frac{1}{x^{2}}y^{-4\left(-1\right)}$$

Multiply -4 times -1.

$$\frac{1}{3}\times \frac{1}{x^{2}}y^{4}$$

Differentiate w.r.t. x

$$-\frac{2y^{4}}{3x^{3}}$$