Integer Exponent Answer Key
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Integer Exponent Properties Guide Answer Key
📚 Part 1: Basic Exponent Properties - ANSWERS
Answer: 3⁶ = 729
Product Rule: When multiplying same bases, add exponents (4 + 2 = 6)
Answer: 5⁴ = 625
Quotient Rule: When dividing same bases, subtract exponents (7 - 3 = 4)
Answer: 2¹² = 4,096
Power Rule: When raising a power to a power, multiply exponents (3 × 4 = 12)
Answer: 1
Zero Exponent Rule: Any non-zero number to the power of 0 equals 1
Answer: 1/6³ = 1/216
Negative Exponent Rule: a⁻ⁿ = 1/aⁿ
✏️ Part 2: Advanced Applications - ANSWERS
Answer: 27x⁶
Apply power to each factor: 3³ × (x²)³ = 27 × x⁶
Answer: 4x³/y⁵
Step-by-step: (8÷2) × (x⁵÷x²) × (y⁻²÷y³) = 4 × x³ × y⁻⁵ = 4x³/y⁵
Answer: a⁶/(4b⁴)
Apply negative exponent: 2⁻² × (a⁻³)⁻² × (b²)⁻² = 1/4 × a⁶ × b⁻⁴
Answer: x = 5
Since 32 = 2⁵, therefore x = 5
🎯 Part 3: Challenge Problems - ANSWERS
Answer: x⁴/y
Work shown:
Step 1: (x⁻²y³)⁻¹ = x²y⁻³
Step 2: (xy⁻¹)² = x²y⁻²
Step 3: x²y⁻³ × x²y⁻² = x⁴y⁻⁵ = x⁴/y⁵
Correction: Final answer is x⁴/y⁵
Answer: x = 2
Since 81 = 3⁴, we have x + 2 = 4, so x = 2
Answer: 8 × 10⁻²
Multiply coefficients: 4 × 2 = 8; Add exponents: 3 + (-5) = -2
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