If x,y,alpha>0 and x>y, then x^(alpha)>y^(alpha)

gasavasiv

gasavasiv

Answered question

2022-10-30

If x , y , α > 0 and x > y, then x α > y α
I know it's obvious when we use differnetation rule for exponential function, but I'm not allowed to. Is there any way I can show it clearly?

Answer & Explanation

Bridget Acevedo

Bridget Acevedo

Beginner2022-10-31Added 19 answers

To compare x α and y α , we can divide the two. ( x y ) α is what you get when you divide the two. Since x > y, ( x y ) > 1. Also, α > 0. When we raise a number greater than 1 to a power greater than 0, we always get a number greater than 1. Therefore, ( x y ) α > 1. This implies that x α > y α

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