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

1 Answer
May 21, 2017

Answer:

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)#