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

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

Evaluate

$$\frac{x^{6}}{9w^{10}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -2.

$$\frac{1}{9}\left(w^{5}\right)^{-2}\left(x^{-3}\right)^{-2}$$

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

$$\frac{1}{9}w^{5\left(-2\right)}x^{-3\left(-2\right)}$$

Multiply 5 times -2.

$$\frac{1}{9}\times \frac{1}{w^{10}}x^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{9}\times \frac{1}{w^{10}}x^{6}$$

Expand

$$\frac{x^{6}}{9w^{10}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -2.

$$\frac{1}{9}\left(w^{5}\right)^{-2}\left(x^{-3}\right)^{-2}$$

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

$$\frac{1}{9}w^{5\left(-2\right)}x^{-3\left(-2\right)}$$

Multiply 5 times -2.

$$\frac{1}{9}\times \frac{1}{w^{10}}x^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{9}\times \frac{1}{w^{10}}x^{6}$$