Question

How do you simplify `(\frac { x ^ { 7} y ^ { 5} } { x y ^ { 5} } ) ^ { 2}`?

Answer 1

`((x^7y^5)/(xy^5))^2=x^12`

Explanation:

`((x^7y^5)/(xy^5))^2`

`color(white)("XXX")=((x^7)/(x) * (y^5)/(y^5))^2`

`color(white)("XXX")=(x^6 * 1)^2`

`color(white)("XXX")=(x^6)^2`

`color(white)("XXX")=x^12`

Answer 2

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the expression and cancel common terms:

`a = a^color(blue)(1)`

`((x^7y^5)/(xy^5))^2 => ((x^7y^5)/(x^color(blue)(1)y^5))^2 => ((x^7color(red)(cancel(color(black)(y^5))))/(x^color(blue)(1)color(red)(cancel(color(black)(y^5)))))^2 => (x^7/x^color(blue)(1))^2`

Next, use this rule of exponents to simplify the term within the parenthesis:

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

`(x^color(red)(7)/x^color(blue)(1))^2 => (x^(color(red)(7)-color(blue)(1)))^2 => (x^6)^2`

Now, use this rule of exponents to complete the simplification:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(x^color(red)(6))^color(blue)(2) => x^(color(red)(6) xx color(blue)(2)) => x^12`