Solve (3p^2/4p^7)^-2

$$( \frac { 3 p ^ { 2 } } { 4 p ^ { 7 } } ) ^ { - 2 }$$

Evaluate

$$\frac{16p^{10}}{9}$$

Solution Steps

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

$$\left(\frac{3}{4p^{5}}\right)^{-2}$$

To raise \frac{3}{4p^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{3^{-2}}{\left(4p^{5}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}}{\left(4p^{5}\right)^{-2}}$$

Expand \left(4p^{5}\right)^{-2}.

$$\frac{\frac{1}{9}}{4^{-2}\left(p^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{\frac{1}{9}}{4^{-2}p^{-10}}$$

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

$$\frac{\frac{1}{9}}{\frac{1}{16}p^{-10}}$$

Express \frac{\frac{1}{9}}{\frac{1}{16}p^{-10}} as a single fraction.

$$\frac{1}{9\times \frac{1}{16}p^{-10}}$$

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

$$\frac{1}{\frac{9}{16}p^{-10}}$$

Expand

$$\frac{16p^{10}}{9}$$

Solution Steps

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

$$\left(\frac{3}{4p^{5}}\right)^{-2}$$

To raise \frac{3}{4p^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{3^{-2}}{\left(4p^{5}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}}{\left(4p^{5}\right)^{-2}}$$

Expand \left(4p^{5}\right)^{-2}.

$$\frac{\frac{1}{9}}{4^{-2}\left(p^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{\frac{1}{9}}{4^{-2}p^{-10}}$$

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

$$\frac{\frac{1}{9}}{\frac{1}{16}p^{-10}}$$

Express \frac{\frac{1}{9}}{\frac{1}{16}p^{-10}} as a single fraction.

$$\frac{1}{9\times \frac{1}{16}p^{-10}}$$

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

$$\frac{1}{\frac{9}{16}p^{-10}}$$