How do you simplify ${(- 2 a b)}^{3} (a c^{3}) (11 b c^{2})$ $(-2ab)^3(ac^3)(11bc^2)$ ?

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How do you simplify ${(- 2 a b)}^{3} (a c^{3}) (11 b c^{2})$ $(-2ab)^3(ac^3)(11bc^2)$ ?

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Answer 1 · 2015-09-24T23:01:53

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

Explanation:

${(- 2 a b)}^{3} (a c^{3}) {(11 b c)}^{2}$ $(-2ab)^3(ac^3)(11bc)^2$

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

${(- 2 a b)}^{3} (a c^{3}) {(11 b c)}^{2} = {(- 2)}^{3} a^{3} b^{3} \times a c^{3} \times {(11)}^{2} b^{2} c^{2}$ $(-2ab)^3(ac^3)(11bc)^2 = (-2)^3a^3b^3 × ac^3 × (11)^2b^2c^2$

$= - 8 a^{3} b^{3} \times a c^{3} \times 121 b^{2} c^{2}$ $= -8a^3b^3 × ac^3 × 121b^2c^2$

Next, we combine like terms.

$- 8 a^{3} b^{3} \times a c^{3} \times 121 b^{2} c^{2}$ $-8a^3b^3 × ac^3 × 121b^2c^2$

$= (- 8 \times 121) \times (a^{3} \times a) \times (b^{3} \times b^{2}) \times (c^{3} \times c^{2})$ $= (-8×121) × (a^3 × a) × (b^3 × b^2) × (c^3 × c^2)$

Now we combine the terms in parentheses again.

Remember that $x^{m} x^{n} = x^{m + n}$ $x^mx^n = x^(m+n)$

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

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

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How do you simplify ${(- 2 a b)}^{3} (a c^{3}) (11 b c^{2})$ $(-2ab)^3(ac^3)(11bc^2)$ ?

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How do you simplify ${(- 2 a b)}^{3} (a c^{3}) (11 b c^{2})$ $(-2ab)^3(ac^3)(11bc^2)$ ?