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calculusxy

  • one year ago

help with exponents. question below.

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  1. calculusxy
    • one year ago
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    \[\large \frac{ (-u^3)^3 }{ u^{-2}v^4 \times -2v^0\times-2u^3v^4 }\]

  2. calculusxy
    • one year ago
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    @Nnesha @phi

  3. Owlcoffee
    • one year ago
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    Do you want to simplify it?

  4. calculusxy
    • one year ago
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    yes

  5. calculusxy
    • one year ago
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    \[\frac{ u^9 }{ u^{-2}v^4\times-2v^0\times-2u^3v^4 }\]

  6. Owlcoffee
    • one year ago
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    Okay, in other words, the expression looks like this: \[\frac{ (-u^3)^3 }{ u ^{-2}v^4(-2v^0)(-2u^3v^4) }\]

  7. calculusxy
    • one year ago
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    i meant to put a -u^9

  8. Owlcoffee
    • one year ago
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    Let's begin by working with the denominator, let's associate all the "v"s and "u"s together sice this does work through the axiom of associative and commutative of multiplication: \[a.b=b.a\] \[a(c.b)=(a.c)b\] So, let's associate the denominator in order to make things clearer: \[\frac{ -u^9 }{ (-2)(u ^{-2})(u^3)(-2)(v^0)(v^4)(v^4) }\] That -2 x -2 can be represented as 4 so: \[\frac{ -u^9 }{ (4)(u ^{-2})(u^3)(v^0)(v^4)(v^4) }\] Now, let's make use of a useful property which has this form: \(a^ma^n=a^{m+n}\) This will allow us to operate those exponents: \[\frac{ -u^9 }{ (4)(u ^{(-2)+3})(v ^{0+4+4}) }\]

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