anonymous
  • anonymous
Friends... Please help me with this one: What is the simplified form of e^x / e^-3x ? I just confuse...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
the answer is e^(4x) right? :)
Owlcoffee
  • Owlcoffee
There is a law of exponents that states something useful: \[\frac{ a^b }{ a^c }=a ^{b-c}\] So, translating it to the problem in question: \[\frac{ e^x }{ e ^{-3x} }=e ^{x-(-3x)}=e ^{x +3x}\]
Owlcoffee
  • Owlcoffee
We can easily prove it by stating the generic division of two exponential numbers: \[\frac{ A ^{y} }{ A ^{x} }\] Let's suppose that \(y>x\) and both belong to the real numbers, so therefore, we can, by definition: \[\frac{ A.A.A.A.A...(y-factors) }{ A.A.A.A.A... (x-factors) }\] Since we have more y factors that x- factors, we will write them like: \[(\frac{ A.A.A.A...(x-factors) }{ A.A.A.A...(x-factors) })((y-x)factors)\] Since the x factors divided x factors are just 1, we remain with the (y-x) factors. \[A.A.A.A...(\left[ y-x \right] factors)\] And by definition of exponents: \[A ^{y-x}\] So, in conclusion, we have just proven that: \[\frac{ A^y}{ A^x }=A ^{y-x}\] Which is a property of the exponents.

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anonymous
  • anonymous
thanks.. :)

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