How do you multiply #(\frac { 3} { 5} a b ^ { - 3} ) ( \frac { 5} { 3} a ^ { - 1} b ^ { 3} )#?

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Answer 1 · 2017-01-28T19:50:00

See the entire solution process below:

First, regroup for like terms:

#(3/5 xx 5/3)(a xx a^-1)(b^-3 xx b^3)#

We can then use the following rules for exponents to simplify:

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

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

#a^color(red)(0) = 1#

#15/15(a^1 xx a^-1)(b^-3 xx b^3) ->#

#1a^(1 + -1)b^(-3 + 3) ->#

#1a^0b^0 ->#

#1 xx 1 xx 1 ->#

#1#