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

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

Evaluate

$$\frac{9}{p^{6}}$$

Solution Steps

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

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

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

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

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

$$\frac{p^{-6}}{3^{-2}}$$

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

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

Divide p^{-6} by \frac{1}{9} by multiplying p^{-6} by the reciprocal of \frac{1}{9}.

$$p^{-6}\times 9$$

Expand

$$\frac{9}{p^{6}}$$

Solution Steps

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

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

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

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

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

$$\frac{p^{-6}}{3^{-2}}$$

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

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

Divide p^{-6} by \frac{1}{9} by multiplying p^{-6} by the reciprocal of \frac{1}{9}.

$$p^{-6}\times 9$$