$y = a^{-x} $

$y = (\frac{1}{a} )^x$

both above graphs are same, plz help understand the exponent property.,.

Question

$y = a^{-x} $

$y = (\frac{1}{a} )^x$

both above graphs are same, plz help understand the exponent property.,.

terenzreignz · Answer

You know that
$$\huge n^{-p}=\frac{1}{n^{p}}$$
?

anonymous · Answer

yes i knw, but im confused about why that works

terenzreignz · Answer

you want me to prove it?

anonymous · Answer

looking at graph of $a^{-x}$  and $a^x$ i see that both are reflections of each other in in y-axis

anonymous · Answer

proof or some reasoning that i can understand is ok...

terenzreignz · Answer

Well, first you have to know that
$$\huge m^{a}m^{b}=m^{a+b}$$

terenzreignz · Answer

You have that, right?

anonymous · Answer

ya that one im ok wid it

terenzreignz · Answer

Ok, so...
$$\huge n^{0}=1$$
right?

anonymous · Answer

yes

terenzreignz · Answer

well
0 = p-p, so...
$$\huge n^{p-p}=1$$

terenzreignz · Answer

right?

anonymous · Answer

ok

anonymous · Answer

how to get to ratio

terenzreignz · Answer

Then, from our property,
$$\huge n^{p}n^{-p}=1$$
right?

anonymous · Answer

wow ! so $n^{-p}$ is multiplicative inverse of $n^p$ which equals to $\frac{1}{n^p}$

terenzreignz · Answer

Yes, that's right :)

terenzreignz · Answer

You get it now?

anonymous · Answer

i get it thank you so soooo much xD

terenzreignz · Answer

No problem :)

anonymous · Answer

turning to this site when i get stuck is much productive than wasting time googling and watching youtube videos hoping my question wil be answered there. appreciate your time very much... . :you guys rock ! xD  , ty