Question

solve for the product a b and c when you put $\frac{\sqrt{4xy^3}}{x^\frac{3}{2}y\frac{7}{2} }$ 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

$\dfrac{\sqrt{4xy^3}}{x^{\frac32} y^{\frac72}} = \sqrt4 \cdot \dfrac{x^{\frac12} y^{\frac32}}{x^{\frac32} y^{\frac72}} = 2x^{\frac12-\frac32} y^{\frac32-\frac72} = 2x^{-1}y^{-2}$

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