What is ((x^{a+b})^2(y^{a+b})^2)/((xy)^{2a-b)} ?

The solution to ((x^{a+b})^2(y^{a+b})^2)/((xy)^{2a-b)} is x^{3b}y^{3b}

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simplify ((x^{a+b})^2(y^{a+b})^2)/((xy)^{2a-b)}

simplify

\frac{( x ^{a + b} ) ^{2} ( y ^{a + b} ) ^{2}}{( x y ) ^{2 a - b}}

x^{3 b} y^{3 b}

Solution steps

\frac{( x ^{a + b} ) ^{2} ( y ^{a + b} ) ^{2}}{( x y ) ^{2 a - b}}

Simplify

(x^{a + b})^{2} (y^{a + b})^{2} : x^{(a + b) \cdot 2} y^{(a + b) \cdot 2}

= \frac{x ^{(a + b) \cdot 2} y ^{(a + b) \cdot 2}}{( x y ) ^{2 a - b}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(x y)^{2 a - b} = x^{2 a - b} y^{2 a - b}

= \frac{x ^{(a + b) \cdot 2} y ^{(a + b) \cdot 2}}{x ^{2 a - b} y ^{2 a - b}}

Simplify

\frac{x ^{(a + b) \cdot 2}}{x ^{2 a - b}} : x^{3 b}

= \frac{x ^{3 b} y ^{(a + b) \cdot 2}}{y ^{2 a - b}}

Simplify

\frac{y ^{(a + b) \cdot 2}}{y ^{2 a - b}} : y^{3 b}

= x^{3 b} y^{3 b}

25 x^{2} - y^{2} + 4 y - 4

3 x^{2} - 13 x y + 12 y^{2}

8^{- 2} q^{3} r^{- 5}

- x - x^{2} - 8 x + 12 < 0

\frac{- 1}{x} < - 2

What is ((x^{a+b})^2(y^{a+b})^2)/((xy)^{2a-b)} ?
The solution to ((x^{a+b})^2(y^{a+b})^2)/((xy)^{2a-b)} is x^{3b}y^{3b}