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

1 Answer
smendyka
Feb 8, 2017

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#

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