Powers
Yes, exponents are the little numbers written up and next to other numbers, the $$3 in the picture above.
Exponents are used simply to indicate that a number is multiplied by itself many times.
For example, $$23 is just another way of writing $$2×2×2.
You may be thinking to yourself how unnecessary exponents are; after all, it's not hard to write $$2×2×2. But suppose you want to write ten $$2's multiplied together. You could either write $$2×2×2×2×2×2×2×2×2×2 or you could simply write $$210. Now suppose you want to write a million $$2's multiplied together... I'm sure you get the picture.
Exponential notation (the notation that involves exponents) is actually very straightforward. Consider $$23. Here the exponent, $$3, tells us how many times the base, $$2, should be used in the multiplication. The following demonstration illustrates more of this notation. Try varying the bases and exponents (by moving the sliders) to see how the numbers change.
A common way to describe exponents is like this:
- $$am means $$a multiplied $$m times
- for example, $$34=3 multiplied $$4 times = $$3×3×3×3
If you find that confusing, you can also think of it this way
- use $$a, $$m times in the multiplication
-
for example, $$34 = use the number $$3, four times in the multiplication = $$3×3×3×3
Examples
Now working out the value of expressions that have exponents is done by remembering what the notation actually means.
Question 1
We want to evaluate $$43 using repeated multiplication. First let's convert $$43 to expanded form. Using the answer from part (a), state the value of $$43.
Here's another one
Question 2
Evaluate $$23×24
Question 3
Write this expression using index notation, in simplest form.
$$5×5