Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

With the function f(x)=x^2 we get a graph like so...


The rule for power functions, that I've been told, is the larger the power gets, the closer the line will touch the x-axis.

Example for f(x)=x^10


My understanding the reason this is, is because no matter how many times you multiply 1/-1 you will always get 1 for the output. So you should always have the parabola curving vertically right at -1/1. That part makes complete sense.

My question is, when you multiply 0.9^200 it equals 7.05...

So, the input 0.9 and output 7.05.. do not seem to stay within the parabola because the parabola doesn't start going vertical till it hits -1/1 on the x-axis..

Am I seeing this right?

share|improve this question
$0.9^{200}\not=7.05$ Rather, $0.9^{200} = 7.05\times10^{-10}$ –  anorton Nov 5 '12 at 23:53
See here: .9^200 –  amWhy Nov 5 '12 at 23:55
@anorton so 7.05 x 10^-10 is not greater than 1? I don't understand how to read 10^-10 –  Tyler Zika Nov 5 '12 at 23:55
10^(-10) = 0.00000000001 –  anorton Nov 5 '12 at 23:57
@anorton Ah ha! That makes complete sense.. Thank you –  Tyler Zika Nov 5 '12 at 23:59

2 Answers 2

Ok. The reason the graph of $y=x^n$ (where $n$ is an even integer) starts to "hug" the x axis for a greater distance as $n$ increases is that multiplying two numbers less than one returns a smaller value.

Essentially: $$x^n < x$$ if $x < 1, n >= 1$

share|improve this answer
up vote 0 down vote accepted

My mistake. 0.9^200 does not equal 7.05. From the calculator, it says 7.05.. x 10^-10. The 10^-10 represents places in the tenths, hundredths, etc. So 0.9^200 does not equal 7.05... but in fact some ridiculously long decimal number in a "-ths" place I can't find a name for.

share|improve this answer
In case anyone wants to know... it is the ten-billion-ths place, if I counted correctly. :) –  anorton Nov 6 '12 at 0:40
@anorton you're awesome –  Tyler Zika Nov 6 '12 at 1:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.