How do you simplify $(36a^8b^2)/(ab)* (6)/(ab^2)^-1$ ?

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Answer 1 · 2015-06-08T17:45:25

$(36a^8b^2)/(ab)* (6)/(ab^2)^color(red)(-1$

$(36a^8b^2)/(a^1b^1)* (6)/(a^(-1)b^-2$

Rearranging the terms:

$((36. 6) (a^8b^2))/((a^1b^1)*(a^(-1)b^-2)$

Note: $color(blue)(a^m/a^n = a^(m-n) and color(blue)(a^m.a^n = a^(m+n)$

applying the above to the exponents of $a$ and $b$

$((36. 6) (a^8b^2))/((a^(1+(-1)) . b^(1+(-2)))$

$((36. 6) (a^8b^2))/((a^(0) b^(-1))$

Note: $color(blue)(a^0 = 1$
$((36. 6) (a^8b^2))/((1. b^(-1))$
$(216) (a^8b^(2-(-1)))$
$=color(red)(216a^8b^3$

How do you simplify (36a^8b^2)/(ab)* (6)/(ab^2)^-1(36a^8b^2)/(ab)* (6)/(ab^2)^-1?