Solve (-1/2a^2b^3)^6

$$( - \frac { 1 } { 2 } a ^ { 2 } b ^ { 3 } ) ^ { 6 }$$

Evaluate

$$\frac{a^{12}b^{18}}{64}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}a^{2}b^{3}\right)^{6}$$

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

$$\left(-\frac{1}{2}\right)^{6}\left(a^{2}\right)^{6}\left(b^{3}\right)^{6}$$

Raise -\frac{1}{2} to the power 6.

$$\frac{1}{64}\left(a^{2}\right)^{6}\left(b^{3}\right)^{6}$$

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

$$\frac{1}{64}a^{2\times 6}b^{3\times 6}$$

Multiply 2 times 6.

$$\frac{1}{64}a^{12}b^{3\times 6}$$

Multiply 3 times 6.

$$\frac{1}{64}a^{12}b^{18}$$

Expand

$$\frac{a^{12}b^{18}}{64}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}a^{2}b^{3}\right)^{6}$$

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

$$\left(-\frac{1}{2}\right)^{6}\left(a^{2}\right)^{6}\left(b^{3}\right)^{6}$$

Raise -\frac{1}{2} to the power 6.

$$\frac{1}{64}\left(a^{2}\right)^{6}\left(b^{3}\right)^{6}$$

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

$$\frac{1}{64}a^{2\times 6}b^{3\times 6}$$

Multiply 2 times 6.

$$\frac{1}{64}a^{12}b^{3\times 6}$$

Multiply 3 times 6.

$$\frac{1}{64}a^{12}b^{18}$$