Cogito
Integrated Math 1 · Chapter 4 · Lesson 3
Properties of Exponents
The rules that make exponentials workable.
12 problems · about 20 minutes · N-RN.A.2, A-SSE.A.2
What this lesson teaches
The student applies the properties of integer exponents to simplify expressions.
- Multiplying adds exponents; dividing subtracts them.
- A power of a power multiplies them.
- A zero exponent gives 1 and a negative exponent gives a reciprocal.
Warm Up
Straightforward practice. Get the method working first.
5 problemsx⁶ · x³ = xⁿ. What is n?
Answer 9
Why 9.
Why does x⁰ equal 1?
Answer Because x³ ÷ x³ is both 1 and x⁰.
Why The quotient rule forces it.
x² · x⁵ = xⁿ. What is n?
Answer 7
Why Add.
x⁹ ÷ x⁴ = xⁿ. What is n?
Answer 5
Why Subtract.
(x²)⁶ = xⁿ. What is n?
Answer 12
Why Multiply.
Build It Up
The same ideas with more to keep track of.
3 problemsWhat is 7⁰?
Answer 1
Why Any non-zero base to the zero.
What is 2⁻³, as a decimal?
Answer 0.125
Why 1 ÷ 8.
x⁴ ÷ x⁶ = xⁿ. What is n?
Answer -2
Why 4 − 6.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each operation with what it does to exponents.
Answer Multiplying powers of the same base → Add the exponents; Dividing powers of the same base → Subtract the exponents; Raising a power to a power → Multiply the exponents
Why Count the factors to see why each rule holds.
What is 5⁻², as a decimal?
Answer 0.04
Why 1 ÷ 25.
The Product: x³ · x⁴ = xⁿ. What is n?
Answer 7
Why 7.
The Power: (x³)⁴ = xⁿ. What is n?
Answer 12
Why 12.