Question

If x^(1/a) = y^(1/5) and xy =1 prove that a=-5

Answer 1

Explanation:

remember :

(x^n)^m = x^(n×m)

and

1/x = x^‐1

therefore, also

1/(x^n) = (1/x)^n = x^-n

now, or situation is

xy = 1

y = 1/x = x^-1

we use this in the original equation

x^(1/a) = y^(1/5) = (1/x)^(1/5) = x^(‐1/5)

so, again

x^(1/a) = x^(‐1/5)

therefore

1/a = -1/5

5/a = -1

5 = -a

a = -5