How do you simplify #u^3v^2*(uv^2)^3# and write it using only positive exponents?

1 Answer
smendyka
Feb 6, 2017

See the entire simplification process below:

Explanation:

First, use these two rules for exponents to expand the term terms within parenthesis:

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

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

#u^3v^2*(uv^2)^3 -> u^3v^2*(u^color(red)(1)v^color(red)(2))^color(blue)(3) -> u^3v^2*(u^(color(red)(1) * color(blue)(3))v^(color(red)(2)*color(blue)(3))) ->#

#u^3v^2*u^3v^6#

Next, rewrite the expression to group like terms:

#u^3u^3 * v^2v^6#

Now, use this rule of exponents to complete the simplification.

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

#u^color(red)(3) xx u^color(blue)(3) * v^color(red)(2) xx v^color(blue)(6) = u^(color(red)(3) +color(blue)(3))v^(color(red)(2) +color(blue)(6)) = #

#u^6v^8#

Because there are no negative exponents there is no further simplification needed.

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