Question

If a power b =b power a show that a/b power a/b = a power a/b-1
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Answer 1

Answer:

Step-by-step explanation:

Given,a^b=b^a

We have to prove that (a/b)^a/b=a^(a/b-1)

Consider LHS:

(a/b)^a/b

= a^(a/b)/b^(a/b)

=a^(a/b)/bth root of b^a

=a^(a/b)/bth root of a^b

=a^(a/b)/a

=a^(a/b-1)

Hence Proved!!