Solve frac{(p^{-6}q^{2})^-2}{(p^4q^-1)^2}

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

Evaluate

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

Solution Steps

Expand \left(p^{-6}q^{2}\right)^{-2}.

$$\frac{\left(p^{-6}\right)^{-2}\left(q^{2}\right)^{-2}}{\left(p^{4}q^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -2 to get 12.

$$\frac{p^{12}\left(q^{2}\right)^{-2}}{\left(p^{4}q^{-1}\right)^{2}}$$

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

$$\frac{p^{12}q^{-4}}{\left(p^{4}q^{-1}\right)^{2}}$$

Expand \left(p^{4}q^{-1}\right)^{2}.

$$\frac{p^{12}q^{-4}}{\left(p^{4}\right)^{2}\left(q^{-1}\right)^{2}}$$

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

$$\frac{p^{12}q^{-4}}{p^{8}\left(q^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{p^{12}q^{-4}}{p^{8}q^{-2}}$$

Cancel out p^{8} in both numerator and denominator.

$$\frac{q^{-4}p^{4}}{q^{-2}}$$

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

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

Expand

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

Solution Steps

Expand \left(p^{-6}q^{2}\right)^{-2}.

$$\frac{\left(p^{-6}\right)^{-2}\left(q^{2}\right)^{-2}}{\left(p^{4}q^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -2 to get 12.

$$\frac{p^{12}\left(q^{2}\right)^{-2}}{\left(p^{4}q^{-1}\right)^{2}}$$

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

$$\frac{p^{12}q^{-4}}{\left(p^{4}q^{-1}\right)^{2}}$$

Expand \left(p^{4}q^{-1}\right)^{2}.

$$\frac{p^{12}q^{-4}}{\left(p^{4}\right)^{2}\left(q^{-1}\right)^{2}}$$

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

$$\frac{p^{12}q^{-4}}{p^{8}\left(q^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{p^{12}q^{-4}}{p^{8}q^{-2}}$$

Cancel out p^{8} in both numerator and denominator.

$$\frac{q^{-4}p^{4}}{q^{-2}}$$

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

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