Cogito
Grade 8 Math · Chapter 7 · Lesson 1
Laws of Exponents
Count the factors and the rules explain themselves.
10 problems · about 19 minutes · 8.EE.A.1
What this lesson teaches
The child applies the properties of integer exponents.
- Multiplying powers of the same base adds the exponents.
- Dividing subtracts them.
- Anything to the power 0 is 1, and a negative exponent is a reciprocal.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Reading a Graph as a Story: A distance graph falls steadily. Is the person moving away or back? 1 for away, 2 for back.
Answer 2
Why Back towards home.
Review — Rate of Change and Starting Value: Through (0, 7) and (3, 19). What is the rate?
Answer 4
Why 4.
Warm Up
Straightforward practice. Get the method working first.
4 problems3⁵ × 3² = 3 to what power?
Answer 7
Why 3⁷.
Why does multiplying powers add the exponents?
Answer You are counting all the factors together.
Why The exponents count factors, so they add.
4² × 4³ = 4 to what power?
Answer 5
Why 2 + 3.
6⁸ ÷ 6³ = 6 to what power?
Answer 5
Why 8 − 3.
Build It Up
The same ideas with more to keep track of.
2 problemsWhat is 7⁰?
Answer 1
Why Anything to the power 0.
What is 2⁻² as a fraction with top 1? Give the bottom number.
Answer 4
Why 1 ÷ 2².
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Product: 2³ × 2² = 2 to what power?
Answer 5
Why 2⁵.
The Quotient: 5⁷ ÷ 5⁴ = 5 to what power?
Answer 3
Why 5³.