Question

How do you multiply `(3x y ) ^ { 4} \cdot 5^ { 0}`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to simplify the 5 term:

`a^color(red)(0) = 1`

`(3xy)^4 * 5^color(red)(0) => (3xy)^4 * 1 => (3xy)^4`

Next, use these rules of exponents to complete the simplification:

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

`(3xy)^4 = (3^color(red)(1)x^color(red)(1)y^color(red)(1))^color(blue)(4) => 3^(color(red)(1)xxcolor(blue)(4))x^(color(red)(1)xxcolor(blue)(4))y^(color(red)(1)xxcolor(blue)(4)) => 3^4x^4y^4 =>`

`51x^4y^4`