Question

solve for the product a b and c when you put
`(√(4xy^3))/(x^(3)/(2)y(7)/(2) )` in the form
`ax^by^c` ?

Answer 1

It helps to write root expressions as rational powers. That is,
`\sqrt[n]{x} = x^(\frac1n)`

Then we have

`(√(4xy^3))/(x^(\frac32) y^(\frac72)) = \sqrt4 \cdot (x^(\frac12) y^(\frac32))/(x^(\frac32) y^(\frac72)) = 2x^(\frac12-\frac32) y^(\frac32-\frac72) = 2x^(-1)y^(-2)`

so that a = 2, b = -1, and c = -2, and thus abc = 4.