Does the 'mAh' rating of a battery have something to do with its power? I'm curious about the 'mAh' of a battery: how can this impact the power of the battery?
I've done some research on the internet, and most of the articles I found explain about the 'amount of charge stored' inside  the battery, or in other words, the 'capacity' of the battery. So the 'mAh' will tell how long the battery can last if a certain amount of current is drawn. But what about the power, does it have anything to do with the power as well? Can anyone explain it?
I'm asking because I have an RC (remote control) car, where usually it uses a Ni-Cd 700 mAh 6V battery. I tried using other batteries; for example I plugged in a standard 6V drycell battery (4 x 1.5V), and it will work, but the car runs very slow, as if it's running under low battery power. Is it because of the 'mAh'? They're the same voltage, 6 volts, but how can the power be different?
I remember a formula from back when I was in school: $V=IR$. So with the internal resistance inside the car, this means the current drawn will be the same. But why can the Ni-Cd battery boost the car?
 A: The mAh hour rating  of a battery is how much energy it stores. It's simply the number of mA it can deliver for an hour (in theory)
The power of a battery is how much energy it can deliver in a certain time. Since Power is current * voltage, and the voltage of a battery is (almost) fixed, then the maximum power is related to the maximum current. Which depends on the internal resistance, which depends on mostly the on the type of battery chemistry and then on the specific design of the electrodes.
So a car battery is designed to produce very high currents (ie high power) to start a car so hasvery low internal resistance, a also NiCad has low internal resistance and so can run a toy car. A disposable battery has highest internal resistance so can produce lowest maximum current and the least power
ps. you can picture the internal resistance as a real resistor built into the battery. Suppose that your dry cell battery has an internal resistance of 2 Ohms and your car's motor has a resistance of 4 Ohms then there is only 4volts of the 6volts from the battery across the motor. Now put in the NiCad with a resistance of 0.1 Ohms and there is 5.9Volts across the motor 
A: I support the answer given by Martin Beckett.
The energy of the battery(that you used) is, 700mAh*6V. The voltage applied across the impedance is constant 6V. Depending on the impedance, the current flows through it. If the current requirement is high(more than 700mA, it runs for 1 hour at that current), you need to get a battery of higher current. Or, you can attach them in parallel. So that, you'll get 700*4mAh. But, the terminal voltage will be 1.5V. So, you need to get 4*4 set of batteries to increase the power delivered to your impedance(motor here).
A: Every battery has a number of basic ratings, such as the nominal terminal voltage and capacity of the battery, typically written somewhere on the battery itself.
The milli-amp-hour rating is a measure of the capacity of the battery, that is, the maximum amount of electric charge which can be 'discharged' from the battery when it is fully charged.
Electric charge is normally measured in coulombs $C$. For example, the charge of a single electron is is $-1.602 \times 10^{-19}C$. For batteries which have a nominally constant voltage, the milli-amp-hour rating is usually quoted for its capacity, the conversion factor being:
$$mA\cdot h = 3.6 \times C$$
In addition to these basic ratings, each battery also has other specific ratings, such as the maximum discharge current (C-rate) and discharge energy (E-rate), usually published in the the manufacturer's data sheets on a series of graphs such as these:

The maximum current capacity which can be discharged from a battery is determined by its 'C-rate'. For example, a rate of 1C means all of the battery current is discharged in 1 hour. A rate of C/10 or 0.1C means discharge current is in 10 hours. 3C means full transfer in 20 minutes. This means the C/10 rate for a battery rated at 1700 mAh is 1700 Ah/10 = 170 mA. A cell's capacity  is not the same at all discharge rates and usually increases with decreasing rate.
The discharge capacity of a battery is the amount of energy discharged from the battery at the rated current and ambient temperature until the discharge end voltage is reached:
$$Energy\space (in\space W\cdot.h )= \frac{Volts \times mA\cdot h}{1000}$$
The amount of electrical power a battery can deliver is the maximum rate at which energy from the battery can be safely discharged, known as the discharge power capability, it is given by the 'E-rate' of the battery. For example, the E/10 rate for a cell or battery rated at 173 watt-hours is 1.73 watts.

When replacing a battery with another type of battery, you must also check the C-rate and E-rate to determine the maximum discharge capacity (current and power) of the battery.
