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 $x^mx^n = x^(m+n)$

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

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

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