When we see repeated addition such as we can rewrite the expression and make it shorter with multiplication. In this case, we get Meanwhile, we can make an expression with repeated multiplication more compact with an exponent. For example, we can rewrite as
What happens when we see a combination of repeated operations in one expression, such as Can we rewrite this expression more simply?
Let's begin by looking at the repeated addition in The term appears four times in the repeated addition, so we can think of it as being multiplied by So,
Is there now some way we can combine the Let's look at the factor first. It means multiplication of three factors of so we can now rewrite the expression as
This is simply So, By switching between the operations of addition, multiplication, and exponentiation, we can make the expression much simpler.
How about an expression such as Can we combine the two terms into one? Let's start by thinking about what and mean. Each represents repeated multiplication of factors of Specifically,
Each term has at least four factors of Let's factor out four factors of from each term. This means we are factoring from each term:
Division by cancels multiplication by so the divided terms simplify:
We can calculate so we can rewrite So,
Are there any exponent rule shortcuts we could have used to make our simplifying more efficient?