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

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Answer 1 · 2017-06-02T14:49:53

See a solution process below:

First, multiply the #x# terms within the parenthesis using this rule for exponents:

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

#(3x^color(red)(2) * x^color(blue)(3))^2 => (3x^(color(red)(2) + color(blue)(3)))^2 => (3x^5)^2#

We can now use these two rules of exponents to complete the multiplication:

#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(3x^5)^2 => (3^color(red)(1)x^color(red)(5))^color(blue)(2) => 3^(color(red)(1) xx color(blue)(2))x^(color(red)(5) xx color(blue)(2)) => 3^2x^10 =>#

#9x^10#