Tutor profile: Adem H.

Why is anything to the power of zero equal to 1?

Pick any two numbers you like for example 4 and 7. Now what is $(\frac{4^{7}}{4^{7}}$) The answer is 1 since any number divided by itself is 1. However, recall that the power rules state that if we divide one number to some power by the same number to a different power, we simply subtract the powers i.e. $$\frac{4^{7}}{4^{7}} =4^{7-7}=4^{0}$$ but we already said that this 4^7/4/7 = 1. Therefore $$4^{0}=1$$ However, this result would have been exactly the same had we chosen any other two numbers apart from 4 and 7.

What is the mole?

The mole is simply a number, just in the same way that a dozen is a number. In this case the number is $6.023\times 10^{23}$. So whenever someone says 1 mole of a certain element they secretly mean that they have $6.023\times 10^{23}$ atoms of that element

Consider the inside of a train carriage. A young boy is inside and notices something peculiar. He sees a fly buzzing around the carriage, what is peculiar is that the fly seems to be flying around in exactly the same manner as when the carriage isn't moving. Despite the train blasting along at high speeds, the fly isn't being thrown to the back of the carriage in mid air. How is this possible?

Provided the train isn't accelerating or going round a sharp corner or bend, the laws of nature, which tell us how things move don't change. This is a key idea in physics that says the laws of physics don't change based up relative motion. If you are in the back set of a car you can still play a game of catch with a friend or sibling, because provided the car doesn't brake, or go round a bend the laws of physics behave the same way as if the car were not moving. The same idea applies to the train carriage as well (this whole idea is known a the Galilean principle of relativity)