Solve (2p^2)^4*(3p^2q)^-2

$$( 2 p ^ { 2 } ) ^ { 4 } \times ( 3 p ^ { 2 } q ) ^ { - 2 }$$

Evaluate

$$\frac{16p^{4}}{9q^{2}}$$

Solution Steps

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

$$2^{4}\left(p^{2}\right)^{4}\times \left(3p^{2}q\right)^{-2}$$

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

$$2^{4}p^{8}\times \left(3p^{2}q\right)^{-2}$$

Calculate 2 to the power of 4 and get 16.

$$16p^{8}\times \left(3p^{2}q\right)^{-2}$$

Expand \left(3p^{2}q\right)^{-2}.

$$16p^{8}\times 3^{-2}\left(p^{2}\right)^{-2}q^{-2}$$

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

$$16p^{8}\times 3^{-2}p^{-4}q^{-2}$$

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

$$16p^{8}\times \frac{1}{9}p^{-4}q^{-2}$$

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

$$\frac{16}{9}p^{8}p^{-4}q^{-2}$$

To multiply powers of the same base, add their exponents. Add 8 and -4 to get 4.

$$\frac{16}{9}p^{4}q^{-2}$$

Expand

$$\frac{16p^{4}}{9q^{2}}$$

Solution Steps

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

$$2^{4}\left(p^{2}\right)^{4}\times \left(3p^{2}q\right)^{-2}$$

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

$$2^{4}p^{8}\times \left(3p^{2}q\right)^{-2}$$

Calculate 2 to the power of 4 and get 16.

$$16p^{8}\times \left(3p^{2}q\right)^{-2}$$

Expand \left(3p^{2}q\right)^{-2}.

$$16p^{8}\times 3^{-2}\left(p^{2}\right)^{-2}q^{-2}$$

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

$$16p^{8}\times 3^{-2}p^{-4}q^{-2}$$

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

$$16p^{8}\times \frac{1}{9}p^{-4}q^{-2}$$

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

$$\frac{16}{9}p^{8}p^{-4}q^{-2}$$

To multiply powers of the same base, add their exponents. Add 8 and -4 to get 4.

$$\frac{16}{9}p^{4}q^{-2}$$