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

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

Evaluate

$$-32b^{10}a^{20}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 5.

$$-32\left(a^{4}\right)^{5}\left(b^{2}\right)^{5}$$

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

$$-32a^{4\times 5}b^{2\times 5}$$

Multiply 4 times 5.

$$-32a^{20}b^{2\times 5}$$

Multiply 2 times 5.

$$-32a^{20}b^{10}$$

Expand

$$-32b^{10}a^{20}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 5.

$$-32\left(a^{4}\right)^{5}\left(b^{2}\right)^{5}$$

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

$$-32a^{4\times 5}b^{2\times 5}$$

Multiply 4 times 5.

$$-32a^{20}b^{2\times 5}$$

Multiply 2 times 5.

$$-32a^{20}b^{10}$$