Numbers expressed as an index or power of a base number are common in chemistry and you need to be confident in manipulating them, both in terms of completing calculations and in being able to simplify equations written in this format.
The number 625 can be expressed as a power of base 5.
It is far more usual though for numbers to be expressed as a power of base 10.
You should also know that any number expressed as a power of ‘1’ is just itself e.g. 51 = 5 and 101 = 10. Similarly, any number expressed to the power of ‘0’ equals 1 e.g. 100 = 1 and 50 = 1.
A negative index means that the number is a fraction (smaller than 1).
A power or index doesn’t have to be an integer (whole number). Two useful ones to recognise are:
If we need to multiply two numbers expressed as a base and an index, we simply add the indices (powers) together.
And if we need to divide two numbers expressed as a base and an index, we subtract the indices (powers) from each other.
The easiest way to check all this for yourself is to play around on your calculator which will also help your learn your way around the function buttons – square roots, cube roots, other roots, positive and negative indices to the power of base 10, positive and negative indices to the power of base x etc.