How do you multiply #(- 5k ^ { 2} j ^ { 4} ) ^ { 3} ( k ^ { 7} j ^ { 7} ) ^ { 3}#?

1 Answer
Feb 4, 2017

Answer:

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis using this rule for exponents:

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

#(-5k^color(red)(2)j^color(red)(4))^color(blue)(3)(k^color(red)(7)j^color(red)(7))^color(blue)(3) = (-5^color(blue)(3)k^(color(red)(2) xx color(blue)(3))j^(color(red)(4) xx color(blue)(3)))(k^(color(red)(7) xx color(blue)(3))j^(color(red)(7) xx color(blue)(3))) =#

#(-125k^6j^12)(k^21j^21)#

Next, rearrange the expression grouping like terms:

#-125(k^6k^21)(j^12j^21)#

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))#

#-125(k^color(red)(6) xx k^color(blue)(21))(j^color(red)(12) xx j^color(blue)(21)) = -125k^(color(red)(6) + color(blue)(21))j^(color(red)(12) + color(blue)(21)) = #

#-125k^27j^33#