Question

if a^b=b^a/,show that (a/b) to the power a/b=a^a/b-1

Answer 1

Answer:

Step-by-step explanation:

LHS= (a/b) to the power a/b =

a^(a/b) /b^(a/b)............ (1)

Let us take the denominator

b^(a/b) = (b power a) ^(1/b)...... (2)

But, b^a =a^b (given)

Substitute this in (2), we get

b^(a/b) = (a^b)^ (1/b) =a^(b x 1/b) =a^1=a.

Substitute this value in (1) we get

LHS = a^(a/b) /a = a^(a/b -1) =RHS

Hence proved.