Find the value of x and y in these equation.

(a^x*b^y) ^ (1/6) = a^ (1/2) * b^ - (1/3)

x=3 y=-2

Step-by-step explanation:

you must take the right part of the equation and express it as (something) ^1/6

you know that the general formula is (a^b) ^c = a^ (b*c)

and (ab) ^c = (a^c) * (b^c)

so you must reach a situation where you express everything ^1/6

a^ (1/2) = a^ (3/6) = (a^3) ^1/6

b^ (-1/3) = b^ (-2/6) = (b^-2) ^1/6

AND

((a^3) ^1/6) * ((b^-2) ^1/6) = (a^3*b^-2) ^1/6

therefore

x=3 and y=-2