Solve (-2w^3x^-6)^5

$$( - 2 w ^ { 3 } x ^ { - 6 } ) ^ { 5 }$$

Evaluate

$$-\frac{32w^{15}}{x^{30}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-2w^{3}x^{-6}\right)^{5}$$

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

$$\left(-2\right)^{5}\left(w^{3}\right)^{5}\left(x^{-6}\right)^{5}$$

Raise -2 to the power 5.

$$-32\left(w^{3}\right)^{5}\left(x^{-6}\right)^{5}$$

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

$$-32w^{3\times 5}x^{-6\times 5}$$

Multiply 3 times 5.

$$-32w^{15}x^{-6\times 5}$$

Multiply -6 times 5.

$$-32w^{15}\times \frac{1}{x^{30}}$$

Expand

$$-\frac{32w^{15}}{x^{30}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-2w^{3}x^{-6}\right)^{5}$$

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

$$\left(-2\right)^{5}\left(w^{3}\right)^{5}\left(x^{-6}\right)^{5}$$

Raise -2 to the power 5.

$$-32\left(w^{3}\right)^{5}\left(x^{-6}\right)^{5}$$

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

$$-32w^{3\times 5}x^{-6\times 5}$$

Multiply 3 times 5.

$$-32w^{15}x^{-6\times 5}$$

Multiply -6 times 5.

$$-32w^{15}\times \frac{1}{x^{30}}$$