Solve (x^{2}pq^2)^2(xp^2)^-1

$$( x ^ { 2 } p q ^ { 2 } ) ^ { 2 } ( x p ^ { 2 } ) ^ { - 1 }$$

Evaluate

$$x^{3}q^{4}$$

Solution Steps

Expand \left(x^{2}pq^{2}\right)^{2}.

$$\left(x^{2}\right)^{2}p^{2}\left(q^{2}\right)^{2}\left(xp^{2}\right)^{-1}$$

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

$$x^{4}p^{2}\left(q^{2}\right)^{2}\left(xp^{2}\right)^{-1}$$

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

$$x^{4}p^{2}q^{4}\left(xp^{2}\right)^{-1}$$

Expand \left(xp^{2}\right)^{-1}.

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

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

$$x^{4}p^{2}q^{4}x^{-1}p^{-2}$$

To multiply powers of the same base, add their exponents. Add 4 and -1 to get 3.

$$x^{3}p^{2}q^{4}p^{-2}$$

Multiply p^{2} and p^{-2} to get 1.

$$x^{3}q^{4}$$

Expand

$$x^{3}q^{4}$$

Solution Steps

Expand \left(x^{2}pq^{2}\right)^{2}.

$$\left(x^{2}\right)^{2}p^{2}\left(q^{2}\right)^{2}\left(xp^{2}\right)^{-1}$$

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

$$x^{4}p^{2}\left(q^{2}\right)^{2}\left(xp^{2}\right)^{-1}$$

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

$$x^{4}p^{2}q^{4}\left(xp^{2}\right)^{-1}$$

Expand \left(xp^{2}\right)^{-1}.

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

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

$$x^{4}p^{2}q^{4}x^{-1}p^{-2}$$

To multiply powers of the same base, add their exponents. Add 4 and -1 to get 3.

$$x^{3}p^{2}q^{4}p^{-2}$$

Multiply p^{2} and p^{-2} to get 1.

$$x^{3}q^{4}$$