What is (x^2pq^2)^2(xp^2)^{-1} ?

The solution to (x^2pq^2)^2(xp^2)^{-1} is x^3q^4

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

simplify

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

x^{3} q^{4}

Solution steps

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

Simplify

(x^{2} p q^{2})^{2} : x^{4} p^{2} q^{4}

= x^{4} p^{2} q^{4} (x p^{2})^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

(x p^{2})^{- 1} = \frac{1}{x p ^{2}}

= x^{4} p^{2} q^{4} \frac{1}{x p ^{2}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{4} p ^{2} q ^{4} \cdot 1}{x p ^{2}}

Apply rule:

a \cdot 1 = a

x^{4} p^{2} q^{4} \cdot 1 = x^{4} p^{2} q^{4}

= \frac{x ^{4} p ^{2} q ^{4}}{x p ^{2}}

Cancel the common factor:

p^{2}

= \frac{x ^{4} q ^{4}}{x}

Simplify

\frac{x ^{4}}{x} : x^{3}

= x^{3} q^{4}

\frac{3 ^{6}}{3 ^{4}}

- 3 x^{2} - 4 x = 0

\frac{6 x ^{- 2} y ^{2}}{3 y ^{- 4}}

6 x^{2} - 2 x = x

(x - 1)^{2} = 49

What is (x^2pq^2)^2(xp^2)^{-1} ?
The solution to (x^2pq^2)^2(xp^2)^{-1} is x^3q^4