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

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Answer 1 · 2017-04-24T21:42:13

See the solution process below:

First, use this rule for equations to simplify the term on the right:

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

#3r^2 * (r^color(red)(3))^color(blue)(3) = 3r^2 * r^(color(red)(3) xx color(blue)(3)) = 3r^2 * r^9#

Next, we can rewrite this expression as:

#3(r^2 * r^9)#

Now, we can 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(r^color(red)(2) xx r^color(blue)(9)) = 3r^(color(red)(2) + color(blue)(9)) = 3r^11#