Solve (-3a^-6b^3)^3

$$( - 3 a ^ { - 6 } b ^ { 3 } ) ^ { 3 }$$

Evaluate

$$-\frac{27b^{9}}{a^{18}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -3 to the power 3.

$$-27\left(a^{-6}\right)^{3}\left(b^{3}\right)^{3}$$

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

$$-27a^{-6\times 3}b^{3\times 3}$$

Multiply -6 times 3.

$$-27\times \frac{1}{a^{18}}b^{3\times 3}$$

Multiply 3 times 3.

$$-27\times \frac{1}{a^{18}}b^{9}$$

Expand

$$-\frac{27b^{9}}{a^{18}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -3 to the power 3.

$$-27\left(a^{-6}\right)^{3}\left(b^{3}\right)^{3}$$

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

$$-27a^{-6\times 3}b^{3\times 3}$$

Multiply -6 times 3.

$$-27\times \frac{1}{a^{18}}b^{3\times 3}$$

Multiply 3 times 3.

$$-27\times \frac{1}{a^{18}}b^{9}$$