Question

How do you simplify `(\frac { x ^ { 7} y ^ { 4} } { x ^ { 3} y ^ { 2} } ) ^ { 2}`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule of exponents to simplify the terms within parenthesis:

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

`((x^color(red)(7)y^color(red)(4))/(x^color(blue)(3)y^color(blue)(2)))^2 = (x^(color(red)(7)-color(blue)(3))y^(color(red)(4)-color(blue)(2)))^2 = (x^4y^2)^2`

Now, use this rule for exponents to eliminate the outer exponent:

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

`(x^color(red)(4)y^color(red)(2))^color(blue)(2) = x^(color(red)(4) xx color(blue)(2))y^(color(red)(2) xx color(blue)(2)) = x^8y^4`