Solve (3w^5x^-2)^-4

$$( 3 w ^ { 5 } x ^ { - 2 } ) ^ { - 4 }$$

Evaluate

$$\frac{x^{8}}{81w^{20}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3w^{5}x^{-2}\right)^{-4}$$

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

$$3^{-4}\left(w^{5}\right)^{-4}\left(x^{-2}\right)^{-4}$$

Raise 3 to the power -4.

$$\frac{1}{81}\left(w^{5}\right)^{-4}\left(x^{-2}\right)^{-4}$$

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

$$\frac{1}{81}w^{5\left(-4\right)}x^{-2\left(-4\right)}$$

Multiply 5 times -4.

$$\frac{1}{81}\times \frac{1}{w^{20}}x^{-2\left(-4\right)}$$

Multiply -2 times -4.

$$\frac{1}{81}\times \frac{1}{w^{20}}x^{8}$$

Expand

$$\frac{x^{8}}{81w^{20}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3w^{5}x^{-2}\right)^{-4}$$

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

$$3^{-4}\left(w^{5}\right)^{-4}\left(x^{-2}\right)^{-4}$$

Raise 3 to the power -4.

$$\frac{1}{81}\left(w^{5}\right)^{-4}\left(x^{-2}\right)^{-4}$$

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

$$\frac{1}{81}w^{5\left(-4\right)}x^{-2\left(-4\right)}$$

Multiply 5 times -4.

$$\frac{1}{81}\times \frac{1}{w^{20}}x^{-2\left(-4\right)}$$

Multiply -2 times -4.

$$\frac{1}{81}\times \frac{1}{w^{20}}x^{8}$$