(a^a)(b^b)u[{(a/b)^b+(b/a)^a}/(a+b)^(a+b)]

asked by guest
on Jan 15, 2025 at 9:17 pm



You asked:

Evaluate the expression: \({a}^{a} {b}^{b} u \cdot \frac{{\left( \frac{a}{b} \right)}^{b} + {\left( \frac{b}{a} \right)}^{a}}{{\left( a + b \right)}^{a + b}}\)

MathBot Answer:

Evaluated



\(\displaystyle {a}^{a} {b}^{b} u \cdot \frac{{\left( \frac{a}{b} \right)}^{b} + {\left( \frac{b}{a} \right)}^{a}}{{\left( a + b \right)}^{a + b}} = a^{a} b^{b} u \left(a + b\right)^{- a - b} \left(\left(\frac{b}{a}\right)^{a} + \left(\frac{a}{b}\right)^{b}\right) \)

Expanded

\[{a}^{a} {b}^{b} u \cdot \frac{{\left( \frac{a}{b} \right)}^{b} + {\left( \frac{b}{a} \right)}^{a}}{{\left( a + b \right)}^{a + b}} = a^{a} b^{b} u \left(\frac{b}{a}\right)^{a} \left(a + b\right)^{- a} \left(a + b\right)^{- b} + a^{a} b^{b} u \left(\frac{a}{b}\right)^{b} \left(a + b\right)^{- a} \left(a + b\right)^{- b}\]

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