Cogito
Grade 8 Math · Chapter 7 · Lesson 3
Zero and Negative Exponents
Continuing the pattern downwards.
10 problems · about 19 minutes · 8.EE.A.1
What this lesson teaches
The child explains why a zero exponent gives 1 and a negative exponent gives a reciprocal.
- Each step down the exponent divides by the base.
- That forces any non-zero number to the power nought to be 1.
- A negative exponent gives a reciprocal, never a negative answer.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Scientific Notation: 3 × 10⁴ written out. What is it?
Answer 30000
Why 30,000.
Review — Laws of Exponents: 3⁵ × 3² = 3 to what power?
Answer 7
Why 3⁷.
Review — 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.
Warm Up
Straightforward practice. Get the method working first.
3 problemsWhat is 10⁻²? Give it as a decimal.
Answer 0.01
Why 0.01.
What is 5⁰?
Answer 1
Why Power nought.
What is 10⁻¹? Give it as a decimal.
Answer 0.1
Why One tenth.
Build It Up
The same ideas with more to keep track of.
2 problemsWhat is 4⁻¹? Give it as a decimal.
Answer 0.25
Why One quarter.
Is 2⁻³ a negative number? 1 for yes, 0 for no.
Answer 0
Why It is one eighth.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Zero Power: What is 7⁰?
Answer 1
Why 1.
The Negative Power: What is 2⁻²? Give it as a decimal.
Answer 0.25
Why ¼, or 0.25.