Cogito
Algebra 1 · Chapter 6 · Lesson 2
Laws of Exponents
Adding, subtracting, and multiplying the powers.
11 problems · about 22 minutes · N-RN.A.2, A-SSE.B.3
What this lesson teaches
The student applies the product, quotient, and power rules for exponents.
- Multiplying like bases adds the exponents; dividing subtracts them.
- A power of a power multiplies them.
- Every rule is just counting factors, which is why writing them out settles any doubt.
Warm Up
Straightforward practice. Get the method working first.
4 problemsx⁷ · x². Exponent?
Answer 9
Why 9.
x³ · x⁶. Exponent?
Answer 9
Why Add.
x⁹ ÷ x⁴. Exponent?
Answer 5
Why Subtract.
(x⁴)³. Exponent?
Answer 12
Why Multiply.
Build It Up
The same ideas with more to keep track of.
3 problemsx⁵ ÷ x⁵. Exponent?
Answer 0
Why Everything cancels.
2³. What is the value?
Answer 8
Why 2 × 2 × 2.
Match each expression to what happens to the exponents.
Answer xᵃ · xᵇ → Add them; xᵃ ÷ xᵇ → Subtract them; (xᵃ)ᵇ → Multiply them
Why Write out the factors if you are unsure.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problems(x³)³. Exponent?
Answer 9
Why 3 × 3.
x⁸ ÷ x². Exponent?
Answer 6
Why 8 − 2.
Multiplying: x⁴ · x⁵. What is the exponent?
Answer 9
Why 9.
A Power of a Power: (x²)⁵. What is the exponent?
Answer 10
Why 10.