Question

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

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`((y * y) * (x^3 * x))^2`

Rewrite the two `y` and one `x` variables using this rule of exponents:

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

`((y^color(red)(1) * y^color(red)(1)) * (x^3 * x^color(red)(1)))^2`

Now, use this rule of exponents to multiply the `x` and the `y` variables:

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

`((y^color(red)(1) * y^color(blue)(1)) * (x^color(red)(3) * x^color(blue)(1)))^2 =>`

`(y^(color(red)(1)+color(blue)(1)) * x^(color(red)(3)+color(blue)(1)))^2 =>`

`(y^2x^4)^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))`

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

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

`y^4x^8` or `x^8y^4`