Solve {left(a^-3b^6c^2/b^-2{c^5}right)}^-3

$${ \left( \frac{ { a }^{ -3 } { b }^{ 6 } { c }^{ 2 } }{ { b }^{ -2 } { c }^{ 5 } } \right) }^{ -3 }$$

Evaluate

$$\frac{\left(ac\right)^{9}}{b^{24}}$$

Solution Steps

Cancel out c^{2} in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{a^{-3}b^{8}}{c^{3}}\right)^{-3}$$

To raise \frac{a^{-3}b^{8}}{c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{-3}b^{8}\right)^{-3}}{\left(c^{3}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\left(a^{-3}b^{8}\right)^{-3}}{c^{-9}}$$

Expand \left(a^{-3}b^{8}\right)^{-3}.

$$\frac{\left(a^{-3}\right)^{-3}\left(b^{8}\right)^{-3}}{c^{-9}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -3 to get 9.

$$\frac{a^{9}\left(b^{8}\right)^{-3}}{c^{-9}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -3 to get -24.

$$\frac{a^{9}b^{-24}}{c^{-9}}$$

Expand

$$\frac{\left(ac\right)^{9}}{b^{24}}$$

Solution Steps

Cancel out c^{2} in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{a^{-3}b^{8}}{c^{3}}\right)^{-3}$$

To raise \frac{a^{-3}b^{8}}{c^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{-3}b^{8}\right)^{-3}}{\left(c^{3}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\left(a^{-3}b^{8}\right)^{-3}}{c^{-9}}$$

Expand \left(a^{-3}b^{8}\right)^{-3}.

$$\frac{\left(a^{-3}\right)^{-3}\left(b^{8}\right)^{-3}}{c^{-9}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -3 to get 9.

$$\frac{a^{9}\left(b^{8}\right)^{-3}}{c^{-9}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -3 to get -24.

$$\frac{a^{9}b^{-24}}{c^{-9}}$$