How do you multiply #a^ { - 5} b ^ { 4} ( a ^ { 3} b ^ { - 2} ) ^ { 3}#?

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Answer 1 · 2016-11-04T09:54:37

#=a^4/b^2#

Recall some of the laws of indices you will need to use

#x^-m = 1/x^m " and "x^m xx x^n = x^(m+n) #

#(xy)^m = x^m xx y^m " and " x^m/x^n = x^(m-n)#

#a^-5b^4color(blue)((a^3b^-2)^3)" "larr# remove the bracket first

#=a^-5b^4 xxcolor(blue)(a^9b^-6)#

#=a^color(red)(-5) b^4 xx a^9b^color(red)(-6)" "larr# remove the negative indices

#=( b^4 xx a^9)/(a^color(red)(5)xxb^color(red)(6))" "larr# simplify indices of like bases

#=a^4/b^2#

Answers are generally given without negative or zero indices.