Question

How do you simplify `sqrt(63x^15 y^9 )/sqrt(7xy^11)`?

Answer 1

See details below

Explanation:

`sqrt(63x^15y^9)/sqrt(7xy^11)=sqrt(9·7(x^7)^2x(y^2)^4y)/(sqrt(7x(y^2)^5y))=(sqrt9cancelsqrt7x^7cancelsqrtxcancely^4cancelsqrty)/(cancelsqrt7cancelsqrtxcancely^4ycancelsqrty)=3x^7/y`

Answer 2

See a solution process below:

Explanation:

First, rewrite the expression using this rule for radicals:

`sqrt(color(red)(a))/sqrt(color(blue)(b)) = sqrt(color(red)(a)/color(blue)(b))`

`sqrt(color(red)(63x^15y^9))/sqrt(color(blue)(7xy^11)) => sqrt(color(red)(63x^15y^9)/color(blue)(7xy^11)) => sqrt((9x^14)/y^2) => (3x^7)/y`