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.
Alabama Course of Study content standard: 8.3 · 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
Exponent Rules in Alabama
In the Alabama Course of Study, this is unit 12 of 17 in 8th grade Math, after Congruent Shapes 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
Simplify 6⁹ ÷ 6⁵.
- 1⁴
- 6²
- 6¹⁴
- 6⁴
6⁴
Hint: When you divide powers with the same base, subtract the exponents.
Question 2
What is 4⁻³?
- −64
- 64
- 1/64
- −1/64
1/64
Hint: A negative exponent means one over: 4⁻³ = 1/4³ = 1/64.
Question 3
Simplify (3⁵)².
- 3⁷
- 6⁵
- 3¹⁰
- 3¹¹
3¹⁰
Hint: A power of a power: multiply the exponents.
Question 4
Simplify 6⁷ × 6².
- 6⁹
- 36⁹
- 6¹⁴
- 6⁵
6⁹
Hint: When you multiply powers with the same base, add the exponents.
Question 5
What is the value of 2⁶ × 2⁻²?
- 16
- 256
- 64
- 32
16
Hint: Add the exponents: 6 + (-2) = 4. 2⁴ = 16.
Question 6
Simplify 2⁸ × 2³.
- 2¹¹
- 2⁵
- 2²⁴
- 4¹¹
2¹¹
Hint: When you multiply powers with the same base, add the exponents.