Solve (frac{P^{2}q^{-1}r^{-2}}{p^4q^4r^-3})^-2

$$( \frac { P ^ { 2 } q ^ { - 1 } r ^ { - 2 } } { p ^ { 4 } q ^ { 4 } r ^ { - 3 } } ) ^ { - 2 }$$

Evaluate

$$\frac{p^{8}q^{10}}{r^{2}P^{4}}$$

Solution Steps

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

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

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

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

Calculate r to the power of 1 and get r.

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

To raise \frac{rP^{2}}{p^{4}q^{5}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{r^{-2}\left(P^{2}\right)^{-2}}{\left(p^{4}q^{5}\right)^{-2}}$$

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

$$\frac{r^{-2}P^{-4}}{\left(p^{4}q^{5}\right)^{-2}}$$

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

$$\frac{r^{-2}P^{-4}}{\left(p^{4}\right)^{-2}\left(q^{5}\right)^{-2}}$$

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

$$\frac{r^{-2}P^{-4}}{p^{-8}\left(q^{5}\right)^{-2}}$$

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

$$\frac{r^{-2}P^{-4}}{p^{-8}q^{-10}}$$

Expand

$$\frac{p^{8}q^{10}}{r^{2}P^{4}}$$

Solution Steps

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

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

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

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

Calculate r to the power of 1 and get r.

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

To raise \frac{rP^{2}}{p^{4}q^{5}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{r^{-2}\left(P^{2}\right)^{-2}}{\left(p^{4}q^{5}\right)^{-2}}$$

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

$$\frac{r^{-2}P^{-4}}{\left(p^{4}q^{5}\right)^{-2}}$$

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

$$\frac{r^{-2}P^{-4}}{\left(p^{4}\right)^{-2}\left(q^{5}\right)^{-2}}$$

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

$$\frac{r^{-2}P^{-4}}{p^{-8}\left(q^{5}\right)^{-2}}$$

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

$$\frac{r^{-2}P^{-4}}{p^{-8}q^{-10}}$$