Laws of Exponents. When multiplying like bases, keep the base the same and add the exponents. When raising a base with power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent. The index of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64. The plural of the index is indices. (Other names for the index are exponent or power.) Chapter 7 takes the students to a new topic Indices [exponents]. If m is a positive integer, then axaxaxa - up to m terms, is written as am; where ‘a’ is called the base and m is called the power (or exponent or index).