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

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

Evaluate

$$\frac{x^{12}}{16w^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power -4.

$$\frac{1}{16}\left(w^{2}\right)^{-4}\left(x^{-3}\right)^{-4}$$

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

$$\frac{1}{16}w^{2\left(-4\right)}x^{-3\left(-4\right)}$$

Multiply 2 times -4.

$$\frac{1}{16}\times \frac{1}{w^{8}}x^{-3\left(-4\right)}$$

Multiply -3 times -4.

$$\frac{1}{16}\times \frac{1}{w^{8}}x^{12}$$

Expand

$$\frac{x^{12}}{16w^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power -4.

$$\frac{1}{16}\left(w^{2}\right)^{-4}\left(x^{-3}\right)^{-4}$$

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

$$\frac{1}{16}w^{2\left(-4\right)}x^{-3\left(-4\right)}$$

Multiply 2 times -4.

$$\frac{1}{16}\times \frac{1}{w^{8}}x^{-3\left(-4\right)}$$

Multiply -3 times -4.

$$\frac{1}{16}\times \frac{1}{w^{8}}x^{12}$$