Question

How do you simplify `sqrt(3x^2y^3)/(4sqrt(5xy^3))`?

Answer 1

See a solution process below:

Explanation:

We can use this rule for dividing radicals to rewrite this expression:

`sqrt(a)/sqrt(b) = sqrt(a/b)`

`sqrt(3x^2y^3)/(4sqrt(5xy^3)) => 1/4sqrt((3x^2y^3)/(5xy^3)) => 1/4sqrt((3x^2color(red)(cancel(color(black)(y^3))))/(5xcolor(red)(cancel(color(black)(y^3))))) =>`

`1/4sqrt((3x^2)/(5x))`

Next, we can use these rules of exponents to simplify the `x` term:

`a^color(red)(1) = a` or `a = a^color(blue)(1)` and `x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`1/4sqrt((3x^2)/(5x)) => 1/4sqrt((3x^color(red)(2))/(5x^color(blue)(1))) => 1/4sqrt((3x^(color(red)(2)-color(blue)(1)))/5) => 1/4sqrt((3x^color(red)(1))/5) =>`

`1/4sqrt((3x)/5)`