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' and means 5 x 5 x 5 x 5.
When we divide numbers with the same base number, we can just subtract the indices.
57 ÷ 53 = 54
This is because, when we divide, we can cancel a 5 on the top with a 5 on the bottom, leaving four 5s on the top.
Does that make sense?
Let's test it out in the questions.