How do you simplify #(-2ab)^3(ac^3)(11bc^2)#?

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Answer 1 · 2015-09-24T23:01:53

#color(red)((-2ab)^3(ac^3)(11bc)^2 = -968a^4b^5c^5)#

#(-2ab)^3(ac^3)(11bc)^2#

You must first apply the outside exponent to everything inside the parentheses.

#(-2ab)^3(ac^3)(11bc)^2 = (-2)^3a^3b^3 × ac^3 × (11)^2b^2c^2#

#= -8a^3b^3 × ac^3 × 121b^2c^2 #

Next, we combine like terms.

#-8a^3b^3 × ac^3 × 121b^2c^2#

#= (-8×121) × (a^3 × a) × (b^3 × b^2) × (c^3 × c^2)#

Now we combine the terms in parentheses again.

Remember that #x^mx^n = x^(m+n)#

#(-8×121) × (a^3 × a) × (b^3 × b^2) × (c^3 × c^2) = -968a^4b^5c^5#

∴ #(-2ab)^3(ac^3)(11bc)^2 = -968a^4b^5c^5 #