How do you simplify ${(- k v)}^{2} {(- k v)}^{3} {(- k v)}^{4}$ $(-kv)^2(-kv)^3(-kv)^4$ ?

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How do you simplify ${(- k v)}^{2} {(- k v)}^{3} {(- k v)}^{4}$ $(-kv)^2(-kv)^3(-kv)^4$ ?

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Answer 1 · 2015-09-29T01:03:09

$- k^{9} v^{9}$ $-k^9v^9$

Explanation:

${(- k v)}^{2} {(- k v)}^{3} {(- k v)}^{4}$ $color(red)((-kv)^2)color(blue)((-kv)^3)color(green)((-kv)^4)$

$XXX = {(- 1)}^{2} k^{2} v^{2} \cdot {(- 1)}^{3} k^{3} v^{3} \cdot {(- 1)}^{4} k^{4} v^{4}$ $color(white)("XXX")=color(red)((-1)^2k^2v^2)*color(blue)((-1)^3k^3v^3)*color(green)((-1)^4k^4v^4)$

$XXX = ({(- 1)}^{2} \cdot {(- 1)}^{3} \cdot {(- 1)}^{4}) \cdot (k^{2} \cdot k^{3} \cdot k^{4}) \cdot (v^{2} \cdot v^{3} \cdot v^{4})$ $color(white)("XXX")=(color(red)((-1)^2) * color(blue)((-1)^3) * color(green)((-1)^4)) * (color(red)(k^2) * color(blue)(k^3) * color(green)(k^4)) * (color(red)(v^2) * color(blue)(v^3) * color(green)(v^4))$

$XXX = {(- 1)}^{9} \cdot k^{9} \cdot v^{9}$ $color(white)("XXX")=(-1)^9 * k^9 * v^9$

$XXX = - k^{9} v^{9}$ $color(white)("XXX")=-k^9v^9$

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How do you simplify ${(- k v)}^{2} {(- k v)}^{3} {(- k v)}^{4}$ $(-kv)^2(-kv)^3(-kv)^4$ ?

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Explanation:

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How do you simplify ${(- k v)}^{2} {(- k v)}^{3} {(- k v)}^{4}$ $(-kv)^2(-kv)^3(-kv)^4$ ?