How do you simplify ${(- 2 x^{4} y^{3})}^{3}$ $(-2x^4y^3)^3$ ?

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How do you simplify ${(- 2 x^{4} y^{3})}^{3}$ $(-2x^4y^3)^3$ ?

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Answer 1 · 2016-02-06T12:49:36

$- 8 x^{12} y^{9}$ $-8x^12y^9$

Explanation:

using the following fact in relation to exponents

${(a^{m})}^{n} = a^{m n}$ $(a^m)^n = a^(mn)$

now apply this to each of the factors

${(- 2 x^{4} y^{3})}^{3} = {(- 2)}^{1 \times 3} . x^{4 \times 3} . y^{3 \times 3}$ $(-2x^4y^3)^3 = (-2)^(1xx3) . x^(4xx3).y^(3xx3)$

$= {(- 2)}^{3} . x^{12} . y^{9} = - 8 x^{12} y^{9}$ $= (-2)^3.x^12.y^9 = -8x^12y^9$

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How do you simplify ${(- 2 x^{4} y^{3})}^{3}$ $(-2x^4y^3)^3$ ?

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How do you simplify ${(- 2 x^{4} y^{3})}^{3}$ $(-2x^4y^3)^3$ ?