What is #-5ab^7 * (-ab^2)#?

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Answer 1 · 2017-09-08T00:40:00

See a solution process below:

First, rewrite the expression as:

#-5ab^7 * (-ab^2) => -5ab^7 * (-1ab^2) => #

#(-5 * -1)(a * a)(b^7 * b^2) => #

#5(a * a)(b^7 * b^2)#

Next, use these rules of exponents to rewrite the #a# terms:

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

#5(a^color(red)(1) * a^color(blue)(1))(b^7 * b^2)#

Now, use this rule of exponents to multiply the #a# and #b# terms:

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

#5(a^color(red)(1) * a^color(blue)(1))(b^color(red)(7) * b^color(blue)(2)) =>#

#5a^(color(red)(1)+color(blue)(1))b^(color(red)(7)+color(blue)(2)) =>#

#5a^2b^9#