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.
Arizona Academic Standards learning standard: A1.A-SSE.A.2 · properties of exponents
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 Arizona
In the Arizona 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.
Source: Arizona Department of Education
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 4³?
answer box
64
Hint: 4³ = 4 × 4 × 4 = 64.
Question 2
What is (−5)⁴?
answer box
625
Hint: Multiply −5 by itself 4 times. An even number of negatives gives a positive answer: 625.
Question 3
Simplify: 7³ × 7⁴
- 49⁷
- 7¹
- 7¹²
- 49¹²
- 7⁷
7⁷
Hint: When you multiply powers with the same base, add the exponents: 3 + 4 = 7.
Question 4
Simplify: 9⁵ ÷ 9²
- 9³
- 9⁴
- 1
- 9⁷
9³
Hint: When you divide powers with the same base, subtract the exponents: 5 − 2 = 3.
Question 5
Simplify: (3⁴)⁴
- 3¹⁷
- 3¹⁶
- 12⁴
- 3²⁵⁶
- 3⁸
3¹⁶
Hint: For a power of a power, multiply the exponents: 4 × 4 = 16.
Question 6
Simplify: x⁶ · x²
- (2x)⁸
- x¹²
- x⁸
- x⁵
- 2x⁸
x⁸
Hint: Same base, so add the exponents: 6 + 2 = 8.