Question

How do you express the following using fractional exponents: `4sqrt(xy+6)sqrt(xy-3)`?

Answer 1

`color(red)( 4sqrt(xy+6)sqrt(xy-3) = 4((xy+6)(xy-3))^(1/2)`

Explanation:

`4sqrt(xy+6)sqrt(xy-3) = 4(xy+6)^(1/2)(xy-3)^(1/2)`

`x^ay^a = (xy)^a`, so

`(xy+6)^(1/2)((xy-3)^(1/2) = ((xy+6)(xy-3))^(1/2)`

∴ `4sqrt(xy+6)sqrt(xy-3) = 4((xy+6)(xy-3))^(1/2)`