/sci/ - Science & Math

1. Something multiplied by it's reciprocal equals 1.

2. Something divided by a number is the same as it being multiplied by its reciprocal.

3. A fraction multiplied by another fraction is the same as their numerators multiplied together divided by their denominators multiplied by each other.

4. A number multiplied by a number divided by a number multiplied by a number is the same as one of the numerators divided by the product of the denominators and the total of that multiplied by the other numerator.

5. A number to the power of a negative number is the same as it's reciprocal to the power of the same power with the opposite sign.

6. A number to the power of a fraction is the same as the root of that number to the degree of the denominator (not sure if I wrote that right) and the product of that to the power of the numerator.

Can anyone explain why instead of just using examples because I can see that examples and proofs work, I just don't understand why they work.