Question

How do you simplify `(\frac { 3x ^ { 5} } { 4y ^ { 8} } ) ^ { 2}`?

Answer 1

See a solution process below:

Explanation:

First, use this rule for exponents to rewrite the expression within the parenthesis:

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

`((3x^5)/(4y^8))^2 => ((3^color(red)(1)x^5)/(4^color(red)(1)y^8))^2`

Next, 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))`

`((3^color(red)(1)x^color(red)(5))/(4^color(red)(1)y^color(red)(8)))^color(blue)(2) => (3^(color(red)(1) xx color(blue)(2))x^(color(red)(5) xx color(blue)(2)))/(4^(color(red)(1) xx color(blue)(2))y^(color(red)(8) xx color(blue)(2))) => (3^2x^10)/(4^2y^16) => (9x^10)/(16y^16)`