Solve (2w^-3x^6)^-2

$$( 2 w ^ { - 3 } x ^ { 6 } ) ^ { - 2 }$$

Evaluate

$$\frac{w^{6}}{4x^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2w^{-3}x^{6}\right)^{-2}$$

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

$$2^{-2}\left(w^{-3}\right)^{-2}\left(x^{6}\right)^{-2}$$

Raise 2 to the power -2.

$$\frac{1}{4}\left(w^{-3}\right)^{-2}\left(x^{6}\right)^{-2}$$

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

$$\frac{1}{4}w^{-3\left(-2\right)}x^{6\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{4}w^{6}x^{6\left(-2\right)}$$

Multiply 6 times -2.

$$\frac{1}{4}w^{6}\times \frac{1}{x^{12}}$$

Expand

$$\frac{w^{6}}{4x^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2w^{-3}x^{6}\right)^{-2}$$

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

$$2^{-2}\left(w^{-3}\right)^{-2}\left(x^{6}\right)^{-2}$$

Raise 2 to the power -2.

$$\frac{1}{4}\left(w^{-3}\right)^{-2}\left(x^{6}\right)^{-2}$$

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

$$\frac{1}{4}w^{-3\left(-2\right)}x^{6\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{4}w^{6}x^{6\left(-2\right)}$$

Multiply 6 times -2.

$$\frac{1}{4}w^{6}\times \frac{1}{x^{12}}$$