Solve (-1/2a^2b^4)^5

$$( - \frac { 1 } { 2 } a ^ { 2 } b ^ { 4 } ) ^ { 5 }$$

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}a^{2}b^{4}\right)^{5}$$

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

$$\left(-\frac{1}{2}\right)^{5}\left(a^{2}\right)^{5}\left(b^{4}\right)^{5}$$

Raise -\frac{1}{2} to the power 5.

$$-\frac{1}{32}\left(a^{2}\right)^{5}\left(b^{4}\right)^{5}$$

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

$$-\frac{1}{32}a^{2\times 5}b^{4\times 5}$$

Multiply 2 times 5.

$$-\frac{1}{32}a^{10}b^{4\times 5}$$

Multiply 4 times 5.

$$-\frac{1}{32}a^{10}b^{20}$$

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}a^{2}b^{4}\right)^{5}$$

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

$$\left(-\frac{1}{2}\right)^{5}\left(a^{2}\right)^{5}\left(b^{4}\right)^{5}$$

Raise -\frac{1}{2} to the power 5.

$$-\frac{1}{32}\left(a^{2}\right)^{5}\left(b^{4}\right)^{5}$$

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

$$-\frac{1}{32}a^{2\times 5}b^{4\times 5}$$

Multiply 2 times 5.

$$-\frac{1}{32}a^{10}b^{4\times 5}$$

Multiply 4 times 5.

$$-\frac{1}{32}a^{10}b^{20}$$