Solve (a^3b^-4c/b^-2)^-6

$$( \frac { a ^ { 3 } b ^ { - 4 } c } { b ^ { - 2 } } ) ^ { - 6 }$$

Evaluate

$$\frac{b^{12}}{c^{6}a^{18}}$$

Solution Steps

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

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

To raise \frac{ca^{3}}{b^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 2 and -6 to get -12.

$$\frac{\left(ca^{3}\right)^{-6}}{b^{-12}}$$

Expand \left(ca^{3}\right)^{-6}.

$$\frac{c^{-6}\left(a^{3}\right)^{-6}}{b^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -6 to get -18.

$$\frac{c^{-6}a^{-18}}{b^{-12}}$$

Expand

$$\frac{b^{12}}{c^{6}a^{18}}$$

Solution Steps

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

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

To raise \frac{ca^{3}}{b^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 2 and -6 to get -12.

$$\frac{\left(ca^{3}\right)^{-6}}{b^{-12}}$$

Expand \left(ca^{3}\right)^{-6}.

$$\frac{c^{-6}\left(a^{3}\right)^{-6}}{b^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -6 to get -18.

$$\frac{c^{-6}a^{-18}}{b^{-12}}$$