How do you multiply #(-4a b ^ { 2})( 9a ^ { 5} b )#?

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Answer 1 · 2017-06-10T22:59:03

See a solution process below:

First, rewrite this expression as:

#(-4 * 9)(a * a^5)(b^2 * b) => -36(a * a^5)(b^2 * b)#

We can now use these rules of exponents to multiply the #a# and #b# terms:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#-36(a * a^5)(b^2 * b) => -36(a^color(red)(1) * a^color(blue)(5))(b^color(red)(2) * b^color(blue)(1)) =>#

#-36(a^(color(red)(1)+color(blue)(5)))(b^(color(red)(2)+color(blue)(1))) =>#

#-36a^6b^3#