How do you simplify ${(- 2 x^{2} y)}^{3} {(5 x y^{3})}^{2}$ $(-2x^2y)^3(5xy^3)^2$ ?

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How do you simplify ${(- 2 x^{2} y)}^{3} {(5 x y^{3})}^{2}$ $(-2x^2y)^3(5xy^3)^2$ ?

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Answer 1 · 2017-12-01T16:27:54

$- 200 x^{8} y^{9}$ $-200x^8y^9$

Explanation:

${(- 2 x^{2} y)}^{3} {(5 x y^{3})}^{2}$ $(-2x^2y)^color(red)3(5xy^3)^color(blue)2$

First, use the exponent rule ${(x^{a})}^{b} = x^{a b}$ $(x^a)^b = x^(ab)$

$({(- 2)}^{3} x^{2 \cdot 3} y^{1 \cdot 3}) (5^{2} x^{1 \cdot 2} y^{3 \cdot 2})$ $((-2)^color(red)3x^(2*color(red)3)y^(1*color(red)3))(5^color(blue)2x^(1*color(blue)2)y^(3*color(blue)2))$

Simplify.

$(- 8 x^{6} y^{3}) (25 x^{2} y^{6})$ $(-8x^6y^3)(25x^2y^6)$

Multiply the coefficients $- 8$ $-8$ and $25$ $25$

$- 200 (x^{6} y^{3}) (x^{2} y^{6})$ $-200(x^color(red)6y^color(blue)3)(x^color(red)2y^color(blue)6)$

Next, use the exponent rule $x^{a} \cdot x^{b} = x^{a b}$ $x^a *x^b = x^(ab)$

$- 200 x^{(6 + 2)} y^{(3 + 6)}$ $-200x^((color(red)(6+2)))y^((color(blue)(3+6)))$

$- 200 x^{8} y^{9}$ $-200x^8y^9$

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How do you simplify ${(- 2 x^{2} y)}^{3} {(5 x y^{3})}^{2}$ $(-2x^2y)^3(5xy^3)^2$ ?

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Explanation:

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How do you simplify (-2x^2y)^3(5xy^3)^2(−2x2y)3(5xy3)2 (-2x^2y)^3(5xy^3)^2?

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How do you simplify ${(- 2 x^{2} y)}^{3} {(5 x y^{3})}^{2}$ $(-2x^2y)^3(5xy^3)^2$ ?