How do you simplify #(36a^8b^2)/(ab)* (6)/(ab^2)^-1#?

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Answer 1 · 2015-06-08T17:45:25

#(36a^8b^2)/(ab)* (6)/(ab^2)^color(red)(-1#

#(36a^8b^2)/(a^1b^1)* (6)/(a^(-1)b^-2#

Rearranging the terms:

#((36. 6) (a^8b^2))/((a^1b^1)*(a^(-1)b^-2)#

Note: #color(blue)(a^m/a^n = a^(m-n) and color(blue)(a^m.a^n = a^(m+n)#

applying the above to the exponents of #a# and #b#

#((36. 6) (a^8b^2))/((a^(1+(-1)) . b^(1+(-2)))#

#((36. 6) (a^8b^2))/((a^(0) b^(-1))#

Note: #color(blue)(a^0 = 1#
#((36. 6) (a^8b^2))/((1. b^(-1))#
#(216) (a^8b^(2-(-1)))#
#=color(red)(216a^8b^3#