Question

How do you simplify `(2v)^2*2v^2` and write it using only positive exponents?

Answer 1

See the entire simplification process below:

Explanation:

First, we will use these two rules for exponents to simplify the term on the left of this expression:

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

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

`(2v)^2 * 2v^2 -> (2^color(red)(1)v^color(red)(1))^color(blue)(2) * 2v^2 -> 2^(color(red)(1) xx color(blue)(2))v^(color(red)(1) xx color(blue)(2)) * 2v^2 -> 2^2v^2 * 2v^2`

We can now use these two rule for exponents to complete the simplification:

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

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

`2^color(red)(2)v^color(red)(2) * 2^color(blue)(1)v^color(blue)(2) -> 2^(color(red)(2)+color(blue)(1))v^(color(red)(2)+color(blue)(2)) -> 2^3v^4 -> 8v^4`