How does Ohm's law work? Can a resistance change depending on the applied voltage? I'm refreshing my memory on electromagnetism, and even though I thought I completely understood Ohm's law, today, while reading my textbook I came across the following.

My question is, what does 'only when referring to materials
or devices for which $R$ is a constant independent of $V$' mean? If $R=\frac{V}{I}$ how can $R$ be independent from $V?$
My other question is as follows. If I have a $2000W$ hairdryer for example, and the $V_{rms}$ voltage over here is $240V$, I would say that the resistance of my hairdryer is $R=\frac{240^2V}{2000W}=28.8\Omega$, but if tomorrow I change country, say, I go to the US, the resistance of my hairdryer would be $R=\frac{120^2V}{2000W}=7.2\Omega$ and therefore the resistance would change, but how can a resistance change? I thought resistors only had a fixed value, like you could go buy a $x\Omega$ resistor and that was it, but how can changing a country change a resistance? Is it because the power I was given was calculated with a $240V$ voltage and for example, in the US the power would be $P=\frac{120^2V}{28.8\Omega}=500W$ but the resistance would still be the same?
Could you clear up my ideas a little please?
 A: In ideal resistor the resistance is constant. However, when you derive the formula V=RI (i.e. see the Drude model) you assume that the electric potential is not too high. The non approximated relationship between current $I$ and the electric potential $v$ is not linear and in this case you can't define R to be constant.
Note that when using resistors, people almost always refer to R as a constant (in real applications, every resistor has some "voltage limit" that people know not to pass, and below this limit the approximation of R as a constant is very good)
A: 
If I have a $2000W$ hairdryer for example, and the $V_{rms}$ voltage over here is $240V$, I would say that the resistance of my hairdryer is $R=\frac{240^2V}{2000W}=28.8\Omega$, but if tomorrow I change country, say, I go to the US, the resistance of my hairdryer would be $R=\frac{120^2V}{2000W}=7.2\Omega$ and therefore the resistance would change,

That is not what would happen. What would happen is that the resistance of the hairdryer would remain the same, 28.8 ohms. So if you used it in the US, it would only consume 500 W, and it would only dry your hair very, very slowly.
I'm ignoring the fact that the heating element in the hairdryer, like the one in an incandescent light bulb, changes resistance in response to its temperature. That effect would mean that actually if you used this hairdryer in the US, its resistance would be lower (because to avoid burning themselves out, the material of the heating element is chosen as one whose resistance increases as it heats up), for example maybe 14 ohms, and therefore it would consume slightly more than the 500 W (1000 W in my example), and maybe wouldn't be quite so bad at drying your hair as a dryer made with a truly linear heating element, but still not nearly as good as when you used it in your home country.
This change in the resistance of the heating element due to its temperature is an example of why real resistors don't have a single "R" value at all times. And in fact it is the same as the example included in the text you quoted when they use the example of the light bulb filament.
A: You can set up $$R=\frac VI$$ and still say that $R$ is constant and independent from $V$ in the same way that you can set up Newton's 2nd law, $$m=\frac Fa, $$ and still say that the mass $m$ is constant and independent from the force. Surely you don't suddenly get heavier just because someone pushes you with a larger force; likewise $R$ doesn't change (for ohmic resistors) just because a larger voltage is applied across it.
Instead what happens is that with a constant $R$, both $V$ and $I$ will always change simultaneously and in the same ratios. That is what Ohm's Law states.
This also answers your other question. If you have a fixed resistance $R$ that you know to be constant, then when the voltage is different in a new country where the power grid output to the wall sockets is different, the power will necessarily have to be different as well for the relationship to still hold true. What actually happens is a reduction in the current along with the voltage reduction, which as per $P=IV$ means a smaller power.
A: Answering to your second question, When you buy an appliance, along with the power rating, the voltage will also be specified. If you use a lesser voltage than the prescribed level the device won't work. The Power and Voltage drawn by device remains constant  . In Layman Terms you can't use a product of your country (with 240V) in America. You will need a step up voltage converter - a device that can be plugged to 120 volts and it provides an outlet with 230 volts for your country's device.
