Power Up Exponents Worksheet
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Pre-Algebra & Grade 6 Expressions
Power Up: Introduction to Exponents
Discover repeated multiplication, anatomy of a power, and exponential notation.
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Anatomy of a Power
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"Five to the third power"
Base (\(5\))
The factor that is multiplied repeatedly.
Exponent (\(3\))
How many times the base is used as a factor.
Common Mistake Trap!
An exponent is NOT regular multiplication with the base!
\( 5^3 \neq 5 \times 3 = 15 \)
\( 5^3 = 5 \times 5 \times 5 = 125 \)
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Special Names to Remember
Power of 2: "Squared" \(x^2\)
\(4^2 = 4 \times 4 = 16\)
Like the area of a square!
Power of 3: "Cubed" \(x^3\)
\(2^3 = 2 \times 2 \times 2 = 8\)
Like the volume of a cube!
Power of 1: "Itself" \(x^1\)
\(9^1 = 9\)
Any base to power 1 is just the base!
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Part A: Complete the Power Chart
Fill in every blank box in each row.
| Word Form | Exponential | Expanded / Repeated Multiplication | Value (Standard) |
|---|
| Three squared (Example) | \(3^2\) | \(3 \times 3\) | \(9\) |
| Two to the fourth power | | | |
| | | |
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| \(6^3\) |
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| \(7 \times 7\) |
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| Ten cubed |
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Part B: Convert Between Forms
Write in Exponential Form (\(b^n\)):
1. \( 8 \times 8 \times 8 \times 8 = \)
2. \( 3 \times 3 \times 3 \times 3 \times 3 = \)
3. \( 11 \times 11 = \)
Write in Expanded Multiplication Form:
4. \( 9^4 = \)
5. \( 4^5 = \)
6. \( 12^3 = \)
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Power Up: Exponents Practice & Applications
PAGE 2 of 2
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Part C: Evaluate Each Power
Expand first, then calculate the standard number value.
7. Evaluate \( 2^5 \) Work:
Value =
8. Evaluate \( 3^4 \) Work:
Value =
9. Evaluate \( 4^3 \) Work:
Value =
10. Evaluate \( 10^4 \) Work:
Value =
11. Evaluate \( 7^2 \) Work:
Value =
12. Evaluate \( 1^{15} \) Work:
Value =
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Part D: Power Showdown (Compare)
Write <, >, or = in the circle. Show values below.
Problem 13
\( 2^4 \)
\( 4^2 \)
Val: ____ Val: ____
Problem 14
\( 3^3 \)
\( 5^2 \)
Val: ____ Val: ____
Problem 15
\( 6^2 \)
\( 2^5 \)
Val: ____ Val: ____
Problem 16
\( 10^3 \)
\( 100^2 \)
Val: ____ Val: ____
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Part E: Spot the Glitch (Error Analysis)
17. Leo's Work:
Leo wrote: \( 2^4 = 8 \)
INCORRECT
What was Leo's mistake?
Correct Value:
18. Maya's Work:
Maya wrote: \( 5 \times 5 \times 5 \times 5 = 4^5 \)
INCORRECT
What was Maya's mistake?
Correct Expression:
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Part F: Real-World Power Challenge (Bacterial Bloom)
STEM Challenge
In a biology lab, a single bacterium doubles into 2 bacteria every hour. After 1 hour there are \(2^1 = 2\) bacteria. After 2 hours there are \(2 \times 2 = 2^2 = 4\) bacteria.
(a) Write the expression for the bacteria count after 6 hours:
Expression:
(b) Calculate the actual total bacteria count after 6 hours:
Total count:
(c) How many hours until there are over 1,000 bacteria?
Hours:
