Solve (frac{12p^{2}q^3}{8p^5q^2})^-2

$$( \frac { 12 p ^ { 2 } q ^ { 3 } } { 8 p ^ { 5 } q ^ { 2 } } ) ^ { - 2 }$$

Evaluate

$$\frac{4p^{6}}{9q^{2}}$$

Solution Steps

Cancel out 4p^{2}q^{2} in both numerator and denominator.

$$\left(\frac{3q}{2p^{3}}\right)^{-2}$$

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

$$\frac{\left(3q\right)^{-2}}{\left(2p^{3}\right)^{-2}}$$

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

$$\frac{3^{-2}q^{-2}}{\left(2p^{3}\right)^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}q^{-2}}{\left(2p^{3}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}q^{-2}}{2^{-2}\left(p^{3}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}q^{-2}}{2^{-2}p^{-6}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{9}q^{-2}}{\frac{1}{4}p^{-6}}$$

Expand

$$\frac{4p^{6}}{9q^{2}}$$

Solution Steps

Cancel out 4p^{2}q^{2} in both numerator and denominator.

$$\left(\frac{3q}{2p^{3}}\right)^{-2}$$

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

$$\frac{\left(3q\right)^{-2}}{\left(2p^{3}\right)^{-2}}$$

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

$$\frac{3^{-2}q^{-2}}{\left(2p^{3}\right)^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}q^{-2}}{\left(2p^{3}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}q^{-2}}{2^{-2}\left(p^{3}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}q^{-2}}{2^{-2}p^{-6}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{9}q^{-2}}{\frac{1}{4}p^{-6}}$$