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anonymous
 one year ago
Friends...
Please help me with this one:
What is the simplified form of e^x / e^3x ?
I just confuse...
anonymous
 one year ago
Friends... Please help me with this one: What is the simplified form of e^x / e^3x ? I just confuse...

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the answer is e^(4x) right? :)

Owlcoffee
 one year ago
Best ResponseYou've already chosen the best response.1There is a law of exponents that states something useful: \[\frac{ a^b }{ a^c }=a ^{bc}\] So, translating it to the problem in question: \[\frac{ e^x }{ e ^{3x} }=e ^{x(3x)}=e ^{x +3x}\]

Owlcoffee
 one year ago
Best ResponseYou've already chosen the best response.1We 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: \[\frac{ A.A.A.A.A...(yfactors) }{ A.A.A.A.A... (xfactors) }\] Since we have more y factors that x factors, we will write them like: \[(\frac{ A.A.A.A...(xfactors) }{ A.A.A.A...(xfactors) })((yx)factors)\] Since the x factors divided x factors are just 1, we remain with the (yx) factors. \[A.A.A.A...(\left[ yx \right] factors)\] And by definition of exponents: \[A ^{yx}\] So, in conclusion, we have just proven that: \[\frac{ A^y}{ A^x }=A ^{yx}\] Which is a property of the exponents.
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