Solve (3w^-4x^3)^-2

$$( 3 w ^ { - 4 } x ^ { 3 } ) ^ { - 2 }$$

Evaluate

$$\frac{w^{8}}{9x^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3w^{-4}x^{3}\right)^{-2}$$

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

$$3^{-2}\left(w^{-4}\right)^{-2}\left(x^{3}\right)^{-2}$$

Raise 3 to the power -2.

$$\frac{1}{9}\left(w^{-4}\right)^{-2}\left(x^{3}\right)^{-2}$$

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

$$\frac{1}{9}w^{-4\left(-2\right)}x^{3\left(-2\right)}$$

Multiply -4 times -2.

$$\frac{1}{9}w^{8}x^{3\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{9}w^{8}\times \frac{1}{x^{6}}$$

Expand

$$\frac{w^{8}}{9x^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3w^{-4}x^{3}\right)^{-2}$$

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

$$3^{-2}\left(w^{-4}\right)^{-2}\left(x^{3}\right)^{-2}$$

Raise 3 to the power -2.

$$\frac{1}{9}\left(w^{-4}\right)^{-2}\left(x^{3}\right)^{-2}$$

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

$$\frac{1}{9}w^{-4\left(-2\right)}x^{3\left(-2\right)}$$

Multiply -4 times -2.

$$\frac{1}{9}w^{8}x^{3\left(-2\right)}$$

Multiply 3 times -2.

$$\frac{1}{9}w^{8}\times \frac{1}{x^{6}}$$