How do you multiply #(3x ^ { \frac { 7} { 2} } ) ^ { 6} ( x ^ { 2} ) ^ { 6}#?

1 Answer
smendyka
Jan 31, 2017

See the entire multiplication process below:

Explanation:

First, use these rules of exponents to begin the multiplication process:

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

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

#(3x^color(red)(7/2))^color(blue)(6)(x^color(red)(2))^color(blue)(6) = (3^color(red)(1)x^color(red)(7/2))^color(blue)(6)(x^color(red)(2))^color(blue)(6) = 3^(color(red)(1) xx color(blue)(6))x^(color(red)(7/2) xx color(blue)(6))x^(color(red)(2) xx color(blue)(6)) =#

#3^6x^21x^12 = 729x^21x^12#

We can now use this rule for exponents to complete the multiplication:

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

#729x^color(red)(21)x^color(blue)(12) = 729x^(color(red)(21) +color(blue)(12)) =#

#729x^33#

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