I'll solve this matching worksheet by simplifying each expression using exponent properties.
Let me work through each problem step by step:
Problem 1: u⁸ × u³ ÷ u⁴
- When multiplying with same base: add exponents → u⁸⁺³ = u¹¹
- When dividing with same base: subtract exponents → u¹¹⁻⁴ = u
- Answer:
u⁷ (matches option e)
Problem 2: s⁶ × s⁷ ÷ s⁸
- Multiply: s⁶⁺⁷ = s¹³
- Divide: s¹³⁻⁸ = s⁵
- Answer:
s⁵ (matches option c)
Problem 3: g⁹ ÷ g⁸ ÷ g²
- First division: g⁹⁻⁸ = g¹
- Second division: g¹⁻² = g⁻¹ = 1/g
- Answer:
1/g (matches option a)
Problem 4: x³ × x⁰ ÷ x⁻⁵
- Remember: x⁰ = 1
- Multiply: x⁻³ × 1 = x⁻³
- Divide: x⁻³⁻⁽⁻⁵⁾ = x⁻³⁺⁵ = x²
- Answer:
x² (matches option i)
Problem 5: y⁻² × y⁻ ÷ y⁻⁹
- Multiply: y⁻²⁺⁽⁻⁶⁾ = y⁻⁸
- Divide: y⁻⁸⁽⁻⁹⁾ = y⁻⁸⁺⁹ = y¹ = y
- Answer:
y (matches option d)
Problem 6: z⁰ / z³
- Remember: z⁰ = 1
- So we have: 1/z³
- Answer:
1/z³ (matches option b)
Problem 7: v⁴ / v⁷
- Subtract exponents: v⁴⁻⁷ = v⁻³ = 1/v³
- Answer:
1/v³ (matches option f)
Problem 8: d⁻¹⁰ / d⁶
- Subtract exponents: d⁻¹⁻⁶ = d⁻¹ = 1/d¹⁶
- Answer:
1/d¹⁶ (matches option h)
Problem 9: h / h⁷
- Subtract exponents: h⁴⁻⁷ = h⁻³ = 1/h³
- Answer:
1/h³ (matches option j)
Problem 10: w⁶ / w⁶
- Subtract exponents: w⁶⁶ = w⁰ = 1
- Answer:
1 (matches option g)
Final Answer:
1-e, 2-c, 3-a, 4-i, 5-d, 6-b, 7-f, 8-h, 9-j, 10-g
Parent Tip: Review the logic above to help your child master the concept of exponent properties worksheet.
