8th grade · Math · Unit 12 of 17
Exponent Rules
Add, subtract, multiply exponents
What your child practices
Properties of integer exponents: multiplying and dividing powers with the same base, a power of a power, zero exponents and negative exponents.
Oregon State Standards learning standard: 8.AEE.A.1 · applying the properties of integer exponents to write equivalent expressions
How we explain it
Children can open this short lesson before they practice.
- Multiply powers with the same base: add the exponents.
- Divide: subtract the exponents. Power of a power: multiply them.
- a⁰ = 1, and a⁻ⁿ = 1/aⁿ.
Example: Simplify 2³ × 2⁴. Same base, so add: 3 + 4 = 7. Answer: 2⁷
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Simplify 4² × 4².
- 4⁴
- 4¹
- 16⁴
4⁴
Hint: When you multiply powers with the same base, add the exponents.
Question 2
What is the value of 2⁶ × 2⁻³?
- 64
- 8
- 512
- 16
8
Hint: Add the exponents: 6 + (-3) = 3. 2³ = 8.
Question 3
What is 5⁻¹?
- 1/5
- −5
- 5
- −1/5
1/5
Hint: A negative exponent means one over: 5⁻¹ = 1/5¹ = 1/5.
Question 4
Simplify (2²)³.
- 2⁶
- 6²
- 2⁵
- 2⁷
2⁶
Hint: A power of a power: multiply the exponents.
Question 5
Simplify 9⁴ ÷ 9³.
- 9¹²
- 1¹
- 9¹
- 9⁷
9¹
Hint: When you divide powers with the same base, subtract the exponents.
Question 6
What is 4⁻²?
- 1/16
- −1/16
- 16
- −16
1/16
Hint: A negative exponent means one over: 4⁻² = 1/4² = 1/16.