Instructions
This worksheet will help you understand and use exponential notation, which is a shortcut for repeated multiplication. Complete the sections in order, showing your work where indicated. Use the ample space provided for calculations.
- Review the definitions in Section 1.
- Complete the tables in Sections 2 and 3.
- Attempt the real-world application problems in Section 4.
- Try the optional Challenge Zone for extra practice.
Section 1: The Power of Notation
Exponential notation consists of two main parts:
- Base: The number being multiplied repeatedly.
- Exponent (or Power): The number that tells you how many times to use the base as a factor.
Example: In the expression $4^3$:
- The Base is 4.
- The Exponent is 3.
- We read this as "Four to the power of three" or "Four cubed."
Task 1: Identify the Parts
Identify the base and exponent for each expression.
| Expression | Base | Exponent |
|---|---|---|
| $2^5$ | 2 | 5 |
| $9^4$ | ||
| $11^2$ | ||
| $6^7$ |
Section 2: Expanding and Condensing
Task 2: Converting Between Forms
Complete the following table by writing the expression in either Expanded Form (repeated multiplication) or Exponential Form (base and power).
| Exponential Form | Expanded Form | Value (Final Answer) |
|---|---|---|
| $2^3$ | 2 x 2 x 2 | 8 |
| $5^2$ | ||
| 4 x 4 x 4 x 4 | ||
| $10^4$ | ||
| 3 x 3 | ||
| $7^1$ | ||
| 6 x 6 x 6 |
Section 3: Evaluating Expressions
Calculate the final value of the following exponential expressions. Show the expanded multiplication step first.
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$3^4$ Expanded: Value:
-
$5^3$ Expanded: Value:
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$1^8$ Expanded: Value:
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$10^5$ Expanded: Value:
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$8^2$ Expanded: Value:
Section 4: Real-World Application (Scaling Up)
Exponential notation helps us describe things that grow or scale quickly, like area, volume, or population growth.
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The Cube Room: A warehouse manager is designing a perfectly cubical storage unit. The length of one side is 4 feet. Write and solve an exponential expression to find the volume of the storage unit (Volume = side x side x side).
Exponential Expression: Calculation: Volume:
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Viral Sharing: A new song is released. On the first day, 2 people share it. On the second day, each of those 2 people shares it with 2 new people (4 shares total). If this pattern continues, how many shares will there be on the 5th day? (Hint: The base is 2.)
Exponential Expression: Calculation: Total Shares on Day 5:
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Area of a Square: A square garden plot has a side length of 12 meters. Area is calculated as side x side, or $s^2$. What is the area of the garden?
Exponential Expression: Area:
Challenge Zone (Optional)
These problems require combining exponent rules with standard order of operations.
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Calculate the value of: $2^4 + 3^2$
Calculation: Value:
-
Solve the expression: $(10 - 7)^3$
Hint: Calculate the value inside the parentheses first.
Calculation: Value:
Answer Key
Section 1: The Power of Notation
| Expression | Base | Exponent |
|---|---|---|
| $2^5$ | 2 | 5 |
| $9^4$ | 9 | 4 |
| $11^2$ | 11 | 2 |
| $6^7$ | 6 | 7 |
Section 2: Expanding and Condensing
| Exponential Form | Expanded Form | Value (Final Answer) |
|---|---|---|
| $2^3$ | 2 x 2 x 2 | 8 |
| $5^2$ | 5 x 5 | 25 |
| $4^4$ | 4 x 4 x 4 x 4 | 256 |
| $10^4$ | 10 x 10 x 10 x 10 | 10,000 |
| $3^2$ | 3 x 3 | 9 |
| $7^1$ | 7 | 7 |
| $6^3$ | 6 x 6 x 6 | 216 |
Section 3: Evaluating Expressions
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$3^4$ Expanded: 3 x 3 x 3 x 3 Value: 81
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$5^3$ Expanded: 5 x 5 x 5 Value: 125
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$1^8$ Expanded: 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 Value: 1
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$10^5$ Expanded: 10 x 10 x 10 x 10 x 10 Value: 100,000
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$8^2$ Expanded: 8 x 8 Value: 64
Section 4: Real-World Application (Scaling Up)
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The Cube Room: Exponential Expression: $4^3$ Calculation: 4 x 4 x 4 = 64 Volume: 64 cubic feet
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Viral Sharing: Exponential Expression: $2^5$ Calculation: 2 x 2 x 2 x 2 x 2 = 32 Total Shares on Day 5: 32
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Area of a Square: Exponential Expression: $12^2$ Area: 144 square meters
Challenge Zone (Optional)
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Calculate the value of: $2^4 + 3^2$ Calculation: (2 x 2 x 2 x 2) + (3 x 3) = 16 + 9 Value: 25
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Solve the expression: $(10 - 7)^3$ Calculation: $(3)^3$ = 3 x 3 x 3 = 27 Value: 27