Solve (a^-2b^-5/c^-11)^-6

$$( \frac { a ^ { - 2 } b ^ { - 5 } } { c ^ { - 11 } } ) ^ { - 6 }$$

Evaluate

$$\frac{a^{12}b^{30}}{c^{66}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{-2}b^{-5}}{c^{-11}}\right)^{-6}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{\left(a^{-2}\right)^{-6}\left(b^{-5}\right)^{-6}}{\left(c^{-11}\right)^{-6}}$$

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

$$\frac{a^{-2\left(-6\right)}b^{-5\left(-6\right)}}{c^{-11\left(-6\right)}}$$

Multiply -2 times -6.

$$\frac{a^{12}b^{-5\left(-6\right)}}{c^{-11\left(-6\right)}}$$

Multiply -5 times -6.

$$\frac{a^{12}b^{30}}{c^{-11\left(-6\right)}}$$

Multiply -11 times -6.

$$\frac{a^{12}b^{30}}{c^{66}}$$

Expand

$$\frac{a^{12}b^{30}}{c^{66}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{-2}b^{-5}}{c^{-11}}\right)^{-6}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{\left(a^{-2}\right)^{-6}\left(b^{-5}\right)^{-6}}{\left(c^{-11}\right)^{-6}}$$

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

$$\frac{a^{-2\left(-6\right)}b^{-5\left(-6\right)}}{c^{-11\left(-6\right)}}$$

Multiply -2 times -6.

$$\frac{a^{12}b^{-5\left(-6\right)}}{c^{-11\left(-6\right)}}$$

Multiply -5 times -6.

$$\frac{a^{12}b^{30}}{c^{-11\left(-6\right)}}$$

Multiply -11 times -6.

$$\frac{a^{12}b^{30}}{c^{66}}$$