Solve (11/4p^-2q^4)^-2

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

Evaluate

$$\frac{16p^{4}}{25q^{8}}$$

Solution Steps

Multiply 1 and 4 to get 4.

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

Add 4 and 1 to get 5.

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

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

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

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

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

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

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

Calculate \frac{5}{4} to the power of -2 and get \frac{16}{25}.

$$\frac{16}{25}p^{4}q^{-8}$$

Expand

$$\frac{16p^{4}}{25q^{8}}$$

Solution Steps

Multiply 1 and 4 to get 4.

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

Add 4 and 1 to get 5.

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

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

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

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

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

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

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

Calculate \frac{5}{4} to the power of -2 and get \frac{16}{25}.

$$\frac{16}{25}p^{4}q^{-8}$$