Recall that exponents are a way of representing repeated multiplication. For example, the notation 54 can be expanded and written as 5 • 5 • 5 • 5, or 625. And don’t forget, the exponent only applies to the number immediately to its left, unless there are parentheses.
What happens if you multiply two numbers in exponential form with the same base? Consider the expression (23)(24). Expanding each exponent, this can be rewritten as (2 • 2 • 2) (2 • 2 • 2 • 2) or 2 • 2 • 2 • 2 • 2 • 2 • 2. In exponential form, you would write the product as 27. Notice, 7 is the sum of the original two exponents, 3 and 4.
What about (x2)(x6)? This can be written as (x • x)(x • x • x • x • x • x) = x • x • x • x • x • x • x • x or x8. And, once again, 8 is the sum of the original two exponents.
