Question

u=x^y then show that (1)uxy=uyx (2)uxyx=uxxy

Answer 1

$u=x^y$ then show that

(1) To show that$uxy = uyx$, we can start by using the definition of u that you provided:$u = x^y.$

Using this definition, we can substitute u for $x^y$ in the equation uxy = uyx:

$x^y * y = y * x^y$

Since multiplication is commutative, meaning the order of the factors doesn't change the result, we can see that $x^y * y$ is equal to $y * x^y.$Therefore, $uxy = uyx.$

(2) To show that uxyx = uxyx, we can again use the definition of u: u = $x^y.$

Using this definition, we can substitute u for $x^y$in the equation uxyx = uxyx:

$x^y * y * x = x^y * x * y$

Here, we can see that $y * x = x * y$, so $x^y * y * x = x^y * x * y$, which means $uxyx = uxyx$

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