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

asked by guest
on Jan 15, 2025 at 9:25 pm



You asked:

Evaluate the expression: aabbu⋅((ab)ba+b+(ba)aa+b)a+b(a+b)a+b{a}^{a} {b}^{b} u \cdot \frac{{\left( {\left( \frac{a}{b} \right)}^{\frac{b}{a + b}} + {\left( \frac{b}{a} \right)}^{\frac{a}{a + b}} \right)}^{a + b}}{{\left( a + b \right)}^{a + b}}

MathBot Answer:

Evaluated



aabbu⋅((ab)ba+b+(ba)aa+b)a+b(a+b)a+b=aabbu(a+b)−a−b((ba)aa+b+(ab)ba+b)a+b\displaystyle {a}^{a} {b}^{b} u \cdot \frac{{\left( {\left( \frac{a}{b} \right)}^{\frac{b}{a + b}} + {\left( \frac{b}{a} \right)}^{\frac{a}{a + b}} \right)}^{a + b}}{{\left( a + b \right)}^{a + b}} = a^{a} b^{b} u \left(a + b\right)^{- a - b} \left(\left(\frac{b}{a}\right)^{\frac{a}{a + b}} + \left(\frac{a}{b}\right)^{\frac{b}{a + b}}\right)^{a + b}

Expanded

aabbu⋅((ab)ba+b+(ba)aa+b)a+b(a+b)a+b=aabbu(a+b)−a(a+b)−b((ba)aa+b+(ab)ba+b)a((ba)aa+b+(ab)ba+b)b{a}^{a} {b}^{b} u \cdot \frac{{\left( {\left( \frac{a}{b} \right)}^{\frac{b}{a + b}} + {\left( \frac{b}{a} \right)}^{\frac{a}{a + b}} \right)}^{a + b}}{{\left( a + b \right)}^{a + b}} = a^{a} b^{b} u \left(a + b\right)^{- a} \left(a + b\right)^{- b} \left(\left(\frac{b}{a}\right)^{\frac{a}{a + b}} + \left(\frac{a}{b}\right)^{\frac{b}{a + b}}\right)^{a} \left(\left(\frac{b}{a}\right)^{\frac{a}{a + b}} + \left(\frac{a}{b}\right)^{\frac{b}{a + b}}\right)^{b}

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