How do you simplify #(4a^3 b^2) (4a^2 b^5)#?

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Answer 1 · 2018-03-19T20:00:04

See a solution process below:

First, rewrite the expression as:

#(4 * 4)(a^3 * a^2)(b^2 * b^5) =>#

#16(a^3 * a^2)(b^2 * b^5)#

Now, use this rule for exponents to simplify the #a# and #b# terms:

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

#16(a^color(red)(3) * a^color(blue)(2))(b^color(red)(2) * b^color(blue)(5)) =>#

#16a^(color(red)(3)+color(blue)(2))b^(color(red)(2)+color(blue)(5)) =>#

#16a^5b^7#