Question

How do you simplify `((3xy^4)/(5z^2))^2`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the expression:

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

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

Now, use this rule of exponents to eliminate the exponent outside the parenthesis:

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

`(9x^2y^8)/(25z^4)`