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

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

Evaluate

$$16a^{16}b^{20}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 4.

$$16\left(a^{4}\right)^{4}\left(b^{5}\right)^{4}$$

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

$$16a^{4\times 4}b^{5\times 4}$$

Multiply 4 times 4.

$$16a^{16}b^{5\times 4}$$

Multiply 5 times 4.

$$16a^{16}b^{20}$$

Expand

$$16a^{16}b^{20}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 4.

$$16\left(a^{4}\right)^{4}\left(b^{5}\right)^{4}$$

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

$$16a^{4\times 4}b^{5\times 4}$$

Multiply 4 times 4.

$$16a^{16}b^{5\times 4}$$

Multiply 5 times 4.

$$16a^{16}b^{20}$$