Negative exponents outside parentheses

[Heather1287]

Hi everyone,

So I am not quite sure how to do negative exponents outside parentheses. My problem is (1+5*10^-10)^-1, and supposedly it simplifies to 1-5*10^-10, but I don't know how that happens. By the way, the 5*10^-10 is scientific notation, and is supposed to remain that way. Please help!

Thanks,
Heather

 

[royhaas]

A negative exponent means the reciprocal of a positive power, so \(\displaystyle (1+5*10^{-10})^{-1} = \frac{1}{(1+5*10^{-10})^{+1}}\).

 

[Deleted member 4993]

That answere comes from an approximation. The approximation being:

\(\displaystyle \frac{1}{1 \, + x} \, = \, 1 - \, x\) [sup:4ugcfmy6].....when x << 1[/sup:4ugcfmy6]

 

[Heather1287]

Thank you!

 

[DrMike]

That answere comes from an approximation. The approximation being:

\(\displaystyle \frac{1}{1 \, + x} \, = \, 1 - \, x\) [sup:30vlu4xn].....when x << 1[/sup:30vlu4xn]

Yes. More exactly, it would be

\(\displaystyle \frac{1}{1 + x} = 1 - x + x^2 - x^3 + x^4 + ...\)

But your x is so close to zero that the terms beyond x[sup:30vlu4xn]2[/sup:30vlu4xn] have just been ignored.