Question

Friends...

Please help me with this one:
What is the simplified form of e^x / e^-3x ?

I just confuse...

Answer 1

the answer is e^(4x) right? :)

Answer 2

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:
\[\frac{ e^x }{ e ^{-3x} }=e ^{x-(-3x)}=e ^{x +3x}\]

Answer 3

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.

Answer 4

thanks.. :)