How do you simplify #(4a^3b^3)(4ab^2)^2# leaving only positive exponents?

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Answer 1 · 2017-02-28T19:57:05

#64a^5b^7#

Split it down into easier parts.

#(4ab^2)^2#

Multiply all the inside indices by #2# because of the #2# on the outside:

#(4ab^2)^2 = 4^2a^2b^4 = 16a^2b^4#

Now we have

#(4a^3b^3)(16a^2b^4)#

You should know that #a^b * a^c = a^(b+c)#, so

#4 * a^3 * b^3 * 16 * a^2 * b^4#

#= 4 * 16 * a^(3+2) * b^(3+4)#

#=64a^5b^7#