M4.1.1 For the adult
Laws of powers
Why is a³ × a⁴ equal to a⁷, and not a¹²?
What this chapter teaches
A power counts copies of a base multiplied together. Joining copies adds the indices, taking some away subtracts them, and groups of groups multiply them. All three laws need the same base.
Three questions to ask
There is no one right wording. Listen for the idea.
- How many a's are multiplied in a³ × a⁴, and how do you know?
- Why do a power of 2 and a power of 3 not combine in 2³ × 3⁴?
- What does the bracket do in (2a²)³, and why is the 2 cubed too?
After the chapter, the learner can
- Simplify a³ × a⁴ and a⁷ ÷ a²
- Simplify (a³)² and (2a²)³
What they copy into their notebook
Same base: multiply, add the indices. Divide, subtract them. Power of a power, multiply them. A bracket powers the number too: (2a²)³ = 8a⁶.