Solve (2a^-4b^5)^5

$$( 2 a ^ { - 4 } b ^ { 5 } ) ^ { 5 }$$

Evaluate

$$\frac{32b^{25}}{a^{20}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2a^{-4}b^{5}\right)^{5}$$

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

$$2^{5}\left(a^{-4}\right)^{5}\left(b^{5}\right)^{5}$$

Raise 2 to the power 5.

$$32\left(a^{-4}\right)^{5}\left(b^{5}\right)^{5}$$

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

$$32a^{-4\times 5}b^{5\times 5}$$

Multiply -4 times 5.

$$32\times \frac{1}{a^{20}}b^{5\times 5}$$

Multiply 5 times 5.

$$32\times \frac{1}{a^{20}}b^{25}$$

Expand

$$\frac{32b^{25}}{a^{20}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2a^{-4}b^{5}\right)^{5}$$

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

$$2^{5}\left(a^{-4}\right)^{5}\left(b^{5}\right)^{5}$$

Raise 2 to the power 5.

$$32\left(a^{-4}\right)^{5}\left(b^{5}\right)^{5}$$

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

$$32a^{-4\times 5}b^{5\times 5}$$

Multiply -4 times 5.

$$32\times \frac{1}{a^{20}}b^{5\times 5}$$

Multiply 5 times 5.

$$32\times \frac{1}{a^{20}}b^{25}$$