I shave every day, but my beard stays the same. What am I?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

Can you find out the remainder when 3^300 is divided by 5?

What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

Find three numbers such that

* When we multiply three numbers, we will get the prime numbers.
* The difference between the second and the first number is equal to the third and second.

What is so fragile that saying its name breaks it?

I have an eye but still cannot see.

Who am I?

What has many teeth, but cannot bite?