Grade 9 Exponents & Powers worksheet
from Gradelings · Name: ______________________
How to explain it
- 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
Question 1
What is 9³?
answer box
729
Hint: 9³ = 9 × 9 × 9 = 729.
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: 8⁵ × 8⁵
- 8²⁵
- 64¹⁰
- 8¹¹
- 8¹⁰
- 64²⁵
8¹⁰
Hint: When you multiply powers with the same base, add the exponents: 5 + 5 = 10.
Question 4
Simplify: 4⁹ ÷ 4⁵
- 1
- 4⁴
- 4²
- 4⁵
- 4¹⁴
4⁴
Hint: When you divide powers with the same base, subtract the exponents: 9 − 5 = 4.
Question 5
Simplify: (3⁵)³
- 3¹⁵
- 3¹⁶
- 9⁵
- 3¹²⁵
- 3⁸
3¹⁵
Hint: For a power of a power, multiply the exponents: 5 × 3 = 15.
Question 6
Simplify: x⁴ · x²
- x⁶
- (2x)⁶
- x³
- x⁸
- 2x⁶
x⁶
Hint: Same base, so add the exponents: 4 + 2 = 6.
Question 7
Which expression is equal to (5x)²?
- 25x
- 10x²
- 5x²
- 25x²
- 5²x
25x²
Hint: Both the 5 and the x are raised to the power 2: (5x)² = 5² × x² = 25x².
Question 8
Write (1/4)³ as a fraction in lowest terms.
answer box
1/64
Hint: Raise the numerator and the denominator to the power 3: 1³/4³ = 1/64, which is 1/64 in lowest terms.
Question 9
Evaluate 2 + 2 × 2².
answer box
10
Hint: Exponents come before multiplication: 2² = 4, then 2 × 4 = 8, then add 2: 10.
Question 10
Which is greater, 2³ or 3²?
- 3²
- They are equal
- 2³
3²
Hint: 2³ = 8 and 3² = 9.
Answer key
- 1. 729
- 2. 625
- 3. 8¹⁰
- 4. 4⁴
- 5. 3¹⁵
- 6. x⁶
- 7. 25x²
- 8. 1/64
- 9. 10
- 10. 3²
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