9th grade · Math · Unit 1 of 17
Exponents & Powers
Exponent laws and scientific notation
What your child practices
Evaluating powers, using the product, quotient and power laws, working with powers of products and fractions, and order of operations with exponents.
Minnesota K-12 Academic Standards benchmark: 9.3.6.8; 9.3.5.2 · the properties of exponents and radicals
How we explain it
Children can open this short lesson before they practice.
- Same base, multiply: add the exponents.
- Same base, divide: subtract the exponents.
- A power of a power multiplies the exponents. Anything to the power 0 is 1.
Example: 2³ × 2⁴ = ? The base is the same, so add the exponents: 3 + 4 = 7. 2⁷ = 128. Answer: 2⁷ = 128
Exponents & Powers in Minnesota
In the Minnesota K-12 Academic Standards, this is unit 1 of 17 in 9th grade Math, before Polynomials.
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 6²?
answer box
36
Hint: 6² = 6 × 6 = 36.
Question 2
What is (−4)²?
answer box
16
Hint: Multiply −4 by itself 2 times. An even number of negatives gives a positive answer: 16.
Question 3
Simplify: 9⁸ × 9³
- 81²⁴
- 9¹¹
- 81¹¹
- 9²⁴
- 9⁵
9¹¹
Hint: When you multiply powers with the same base, add the exponents: 8 + 3 = 11.
Question 4
Simplify: 2¹¹ ÷ 2⁵
- 2⁶
- 2⁷
- 1
- 2¹⁶
- 2²
2⁶
Hint: When you divide powers with the same base, subtract the exponents: 11 − 5 = 6.
Question 5
Simplify: (6⁴)⁵
- 6²¹
- 30⁴
- 6²⁰
- 6¹⁰²⁴
- 6⁹
6²⁰
Hint: For a power of a power, multiply the exponents: 4 × 5 = 20.
Question 6
Simplify: x³ · x⁷
- x²¹
- x¹⁰
- 2x¹⁰
- (2x)¹⁰
- x⁵
x¹⁰
Hint: Same base, so add the exponents: 3 + 7 = 10.