How do you multiply #3n ^ { 3} \cdot ( n ^ { 2} ) ^ { 3}#?

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Answer 1 · 2017-04-17T20:59:39

See the entire solution process below:

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

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

#3n^3 * (n^color(red)(2))^color(blue)(3) = 3n^3 * n^(color(red)(2) xx color(blue)(3)) = 3n^3 * n^6#

Next, rewrite the expression as:

#3(n^3 * n^6)#

Now, use this rule of exponents to complete the multiplication:

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

#3(n^color(red)(3) xx x^color(blue)(6)) = 3n^(color(red)(3) + color(blue)(6)) = 3n^9#