Solve (4p^2/3p^6)^-2

$$( \frac { 4 p ^ { 2 } } { 3 p ^ { 6 } } ) ^ { - 2 }$$

Evaluate

$$\frac{9p^{8}}{16}$$

Solution Steps

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

$$\left(\frac{4}{3p^{4}}\right)^{-2}$$

To raise \frac{4}{3p^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{4^{-2}}{\left(3p^{4}\right)^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\left(3p^{4}\right)^{-2}}$$

Expand \left(3p^{4}\right)^{-2}.

$$\frac{\frac{1}{16}}{3^{-2}\left(p^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\frac{1}{16}}{3^{-2}p^{-8}}$$

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

$$\frac{\frac{1}{16}}{\frac{1}{9}p^{-8}}$$

Express \frac{\frac{1}{16}}{\frac{1}{9}p^{-8}} as a single fraction.

$$\frac{1}{16\times \frac{1}{9}p^{-8}}$$

Multiply 16 and \frac{1}{9} to get \frac{16}{9}.

$$\frac{1}{\frac{16}{9}p^{-8}}$$

Expand

$$\frac{9p^{8}}{16}$$

Solution Steps

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

$$\left(\frac{4}{3p^{4}}\right)^{-2}$$

To raise \frac{4}{3p^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{4^{-2}}{\left(3p^{4}\right)^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\left(3p^{4}\right)^{-2}}$$

Expand \left(3p^{4}\right)^{-2}.

$$\frac{\frac{1}{16}}{3^{-2}\left(p^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\frac{1}{16}}{3^{-2}p^{-8}}$$

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

$$\frac{\frac{1}{16}}{\frac{1}{9}p^{-8}}$$

Express \frac{\frac{1}{16}}{\frac{1}{9}p^{-8}} as a single fraction.

$$\frac{1}{16\times \frac{1}{9}p^{-8}}$$

Multiply 16 and \frac{1}{9} to get \frac{16}{9}.

$$\frac{1}{\frac{16}{9}p^{-8}}$$