What is (e^{-x-y})^2(e^{xy})^2 ?

The solution to (e^{-x-y})^2(e^{xy})^2 is e^{2(xy-x-y)}

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simplify (e^{-x-y})^2(e^{xy})^2

simplify

(e^{- x - y})^{2} (e^{x y})^{2}

e^{2 (x y - x - y)}

Solution steps

(e^{- x - y})^{2} (e^{x y})^{2}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

(e^{x y})^{2} (e^{- x - y})^{2} = (e^{- x - y} e^{x y})^{2}

= (e^{- x - y} e^{x y})^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- x - y} e^{x y} = e^{- x - y + x y}

= (e^{- x - y + x y})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= e^{(- x - y + x y) \cdot 2}

e^{- \frac{b}{0.5}}

e^{- t} \cdot e^{- 5 t}

- 2 e^{- 2 y}

6^{- 3 \circ} 6^{- 6}

4800 e^{- 2}

What is (e^{-x-y})^2(e^{xy})^2 ?
The solution to (e^{-x-y})^2(e^{xy})^2 is e^{2(xy-x-y)}