9th grade · Math · Unit 2 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.
Washington State Learning Standards learning standard: M.HS.Q.ASSE.2 · rewriting expressions with powers using the exponent laws
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
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 8³?
answer box
512
Hint: 8³ = 8 × 8 × 8 = 512.
Question 2
What is (−5)³?
answer box
-125
Hint: Multiply −5 by itself 3 times. An odd number of negatives gives a negative answer: -125.
Question 3
Simplify: 9⁶ × 9⁶
- 9³⁶
- 9¹³
- 81³⁶
- 81¹²
- 9¹²
9¹²
Hint: When you multiply powers with the same base, add the exponents: 6 + 6 = 12.
Question 4
Simplify: 5¹⁰ ÷ 5⁶
- 5¹⁶
- 5²
- 5⁴
- 5⁵
- 1
5⁴
Hint: When you divide powers with the same base, subtract the exponents: 10 − 6 = 4.
Question 5
Simplify: (7⁵)²
- 7¹⁰
- 7¹¹
- 14⁵
- 7²⁵
- 7⁷
7¹⁰
Hint: For a power of a power, multiply the exponents: 5 × 2 = 10.
Question 6
Simplify: x⁶ · x³
- x⁹
- x⁴
- x¹⁸
- 2x⁹
- (2x)⁹
x⁹
Hint: Same base, so add the exponents: 6 + 3 = 9.