Power Play Warmup Worksheet
Algebra 1 Warm-up
POWER PLAY
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Directions: Simplify each algebraic expression by applying the distributive property and the product rule for exponents. Write your final simplified expression clearly in the workspace box on the right. Show all intermediate steps.
01 Level 1
\[ x^3 (x^2 + x^4) \]
Workspace & Answer
02 Level 1
\[ x^2 (x^5 - x^3) \]
Workspace & Answer
03 Level 2
\[ 3x^4 (x^2 + 2x^3) \]
Workspace & Answer
04 Level 2
\[ 2x^3 (4x^2 - x^5) \]
Workspace & Answer
05 Level 3
\[ 4x^5 (2x^2 + 3x^3) \]
Workspace & Answer
Unit 2: Exponent Rules & Operations Page 1 of 1
Power Play Warmup Answer Key
Teacher Resource
POWER PLAY ANSWER KEY
Solutions & Guide
Instructional Notes: Use this guide to quickly grade or review solutions. The workspace highlights step-by-step expansion and notes common pitfalls where students confuse multiplying bases with multiplying exponents.
01 Level 1
\[ x^3 (x^2 + x^4) \]
Step-by-Step Solution
\( = x^3 \cdot x^2 + x^3 \cdot x^4 \)
\( = x^{3+2} + x^{3+4} \)
\( \rightarrow \) Final Answer: \( x^5 + x^7 \)
Watch for: Students multiplying exponents to get \( x^6 + x^{12} \).
02 Level 1
\[ x^2 (x^5 - x^3) \]
Step-by-Step Solution
\( = x^2 \cdot x^5 - x^2 \cdot x^3 \)
\( = x^{2+5} - x^{2+3} \)
\( \rightarrow \) Final Answer: \( x^7 - x^5 \)
Watch for: Forgetting the minus sign; or writing \( x^{10} - x^6 \).
03 Level 2
\[ 3x^4 (x^2 + 2x^3) \]
Step-by-Step Solution
\( = (3x^4 \cdot x^2) + (3x^4 \cdot 2x^3) \)
\( = 3x^{4+2} + (3 \cdot 2)x^{4+3} \)
\( \rightarrow \) Final Answer: \( 3x^6 + 6x^7 \)
Watch for: Forgetting to multiply coefficients (\( 3 \cdot 2 \)) or adding coefficients instead.
04 Level 2
\[ 2x^3 (4x^2 - x^5) \]
Step-by-Step Solution
\( = (2x^3 \cdot 4x^2) - (2x^3 \cdot x^5) \)
\( = (2 \cdot 4)x^{3+2} - 2x^{3+5} \)
\( \rightarrow \) Final Answer: \( 8x^5 - 2x^8 \)
Watch for: Dropping the coefficient of 2 in the second term; or writing \( 8x^5 - 2x^{15} \).
05 Level 3
\[ 4x^5 (2x^2 + 3x^3) \]
Step-by-Step Solution
\( = (4x^5 \cdot 2x^2) + (4x^5 \cdot 3x^3) \)
\( = 8x^{5+2} + 12x^{5+3} \)
\( \rightarrow \) Final Answer: \( 8x^7 + 12x^8 \)
Watch for: Adding coefficients (\( 4+2=6, 4+3=7 \)) or multiplying exponents (\( 5 \cdot 2=10, 5 \cdot 3=15 \)).
Unit 2: Exponent Rules & Operations Teacher Answer Key
