Solve (2w^6x^-2)^5

$$( 2 w ^ { 6 } x ^ { - 2 } ) ^ { 5 }$$

Evaluate

$$\frac{32w^{30}}{x^{10}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2w^{6}x^{-2}\right)^{5}$$

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

$$2^{5}\left(w^{6}\right)^{5}\left(x^{-2}\right)^{5}$$

Raise 2 to the power 5.

$$32\left(w^{6}\right)^{5}\left(x^{-2}\right)^{5}$$

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

$$32w^{6\times 5}x^{-2\times 5}$$

Multiply 6 times 5.

$$32w^{30}x^{-2\times 5}$$

Multiply -2 times 5.

$$32w^{30}\times \frac{1}{x^{10}}$$

Expand

$$\frac{32w^{30}}{x^{10}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2w^{6}x^{-2}\right)^{5}$$

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

$$2^{5}\left(w^{6}\right)^{5}\left(x^{-2}\right)^{5}$$

Raise 2 to the power 5.

$$32\left(w^{6}\right)^{5}\left(x^{-2}\right)^{5}$$

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

$$32w^{6\times 5}x^{-2\times 5}$$

Multiply 6 times 5.

$$32w^{30}x^{-2\times 5}$$

Multiply -2 times 5.

$$32w^{30}\times \frac{1}{x^{10}}$$