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

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

Evaluate

$$\frac{1}{8\left(ab\right)^{6}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

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

Expand \left(2a^{2}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

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

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}a^{-6}}{b^{6}}$$

Expand

$$\frac{1}{8\left(ab\right)^{6}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

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

Expand \left(2a^{2}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

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

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}a^{-6}}{b^{6}}$$