An index is sometimes called a power or an exponent.
In 54, the 4 is the index and the 5 is the base.
54 is read as "5 to the power 4" or "5 to the 4" and means 5 x 5 x 5 x 5.
Multiplying numbers
When we multiply numbers with the same base number, we can just add the indices.
54 x 53 = 57
This is because 5 x 5 x 5 x 5 x 5 x 5 x 5 = 57