Question

How do you simplify `((3x^7)/(2y^12))^4` and write it using only positive exponents?

Answer 1

See a solution process below:

Explanation:

Use, these rules of exponents to simplify the expression:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`((3x^7)/(2y^12))^4 => ((3^color(red)(1)x^color(red)(7))/(2^color(red)(1)y^color(red)(12)))^color(blue)(4) => (3^(color(red)(1)xxcolor(blue)(4))x^(color(red)(7)xxcolor(blue)(4)))/(2^(color(red)(1)xxcolor(blue)(4))y^(color(red)(12)xxcolor(blue)(4))) => (3^4x^28)/(2^4y^48) =>`

`(81x^28)/(16y^48)`