Power Up Practice Worksheet
Pre-Algebra & Grade 6-8 Math
POWER UP: EXPONENT BASICS
Name:
Date:
Class: Score:
Anatomy of a Power
\(b^e\)
Base (\(b\)): Factor repeated
Exponent (\(e\)): Times multiplied
Connecting Repeated Multiplication
Exponential \(3^4\)
=
Repeated Factors \(3 \times 3 \times 3 \times 3\)
=
Standard Form 81
1 Part 1: Deconstruct the Power
Fill in every missing cell in the table below.
| Exponential Form | Base | Exponent | Repeated Multiplication (Expanded) | Standard Value |
|---|
| \(2^4\) (example) | 2 | 4 | \(2 \times 2 \times 2 \times 2\) | 16 |
| \(5^3\) | | | | |
| 4 | 2 | | |
| \(10^4\) | | | | |
| | | \(7 \times 7\) | |
| \(3^5\) | | | | |
2 Part 2: Express in Exponential Form
Rewrite each repeated multiplication using base and exponent notation. Do not evaluate yet.
- \(6 \times 6 \times 6\)
Answer:
- \(8 \times 8 \times 8 \times 8 \times 8\)
Answer:
- \(12 \times 12\)
Answer:
- \(y \cdot y \cdot y \cdot y\)
Answer:
- \(2 \times 2 \times 2 \times 2 \times 2 \times 2\)
Answer:
- \(9 \times 9 \times 9 \times 9\)
Answer:
Key Rule: An exponent tells how many times the base is used as a factor—NOT to multiply base by exponent! Page 1 of 2
Page 2
POWER UP: PRACTICE & APPLICATION
Student Name:
3 Part 3: Evaluate Each Power (Show All Steps)
Write out the repeated multiplication first, then compute the final numerical value.
7. Evaluate \(2^5\) Value: _______
Repeated multiplication:
Work area:
8. Evaluate \(4^3\) Value: _______
Repeated multiplication:
Work area:
9. Evaluate \(6^3\) Value: _______
Repeated multiplication:
Work area:
10. Evaluate \(10^5\) Value: _______
Repeated multiplication:
Work area:
4 Part 4: Compare Powers (\(<\), \(>\), or \(=\))
Calculate the value of each side, show your calculation below, then write the correct comparison symbol in the circle.
11. \(2^4\) \(4^2\)
Value of \(2^4\):
Value of \(4^2\):
12. \(3^3\) \(2^5\)
Value of \(3^3\):
Value of \(2^5\):
13. Detective: Fix the Error
Jordan claims that \(5^3 = 15\) because \(5 \times 3 = 15\).
What misconception did Jordan make?
Correct Value of \(5^3\):
14. Real-World Growth
A single amoeba cell divides into 2 cells every hour. After 6 hours, the number of cells is represented by \(2^6\).
Write as repeated multiplication:
Total number of cells after 6 hours:
Remember: \(b^0 = 1\) (for \(b \neq 0\)) and \(b^1 = b\). Always expand when unsure! Page 2 of 2
