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

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

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

$=64a^5b^7$

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