8th grade · Math · Unit 8 of 11
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.
Minnesota K-12 Academic Standards benchmark: 8.3.5.3 · the properties of integer exponents
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
Exponent Rules in Minnesota
In the Minnesota K-12 Academic Standards, this is unit 8 of 11 in 8th grade Math, after Equations with Brackets and before Systems of Equations.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
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
What is 5⁻²?
- −25
- 25
- 1/25
- −1/25
1/25
Hint: A negative exponent means one over: 5⁻² = 1/5² = 1/25.
Question 2
What is the value of 3³ × 3⁻¹?
- 8
- 27
- 81
- 9
9
Hint: Add the exponents: 3 + (-1) = 2. 3² = 9.
Question 3
Simplify (7²)³.
- 21²
- 7⁶
- 7⁵
- 7⁷
7⁶
Hint: A power of a power: multiply the exponents.
Question 4
Simplify 4⁹ ÷ 4⁵.
- 1⁴
- 4¹⁴
- 4²
- 4⁴
4⁴
Hint: When you divide powers with the same base, subtract the exponents.
Question 5
Simplify 2³ × 2⁴.
- 2⁷
- 2¹²
- 2¹
- 4⁷
2⁷
Hint: When you multiply powers with the same base, add the exponents.
Question 6
Simplify 7⁶ × 7⁶.
- 49¹²
- 7¹²
- 7³⁶
- 7¹
7¹²
Hint: When you multiply powers with the same base, add the exponents.