A Definition And A Rule
Introduction, Stage 5 – Feel the Power
The definition
Just as 4 × 2 is a quick way to write 2 + 2 + 2 + 2, so 24 is a quick way to write 2 × 2 × 2 × 2. It’s much easier to say and understand the phrase “two to the fourth,” than to say “two times two times … “
Special names
The second power, 42 for example, can be said four squared, and the third power, 43 for example, can be said four cubed.
The rule
When powers of the same number are multiplied, a simple rule governs how to simplify the result – add the powers. For example, if you do 42 × 43 = (4 × 4) × (4 × 4 × 4) = 45, we have two fours multiplied by three fours, so the result is five fours being multiplied.
Caution
Note that this rule for adding exponents only works when it is the same number being taken to a power – you can’t easily simplify 32 × 53.