You’re working on
Exponents – Quotient Rule. The quotient rule for exponents says:
> When dividing two expressions with the same base, subtract the exponent in the denominator from the exponent in the numerator:
>
>
aᵐ / aⁿ = aᵐ⁻ⁿ
Also, remember: if the result is a negative exponent, rewrite it as a positive exponent by moving the term to the other part of the fraction (numerator ↔ denominator).
Let’s solve each problem step by step.
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a) e⁸ / e³
→ Subtract exponents: 8 - 3 = 5
✔ Answer: e⁵
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b) y⁷ / y⁷
→ 7 - 7 = 0 → Any non-zero number to the power 0 is 1
✔ Answer: 1
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c) u⁴ / u⁶
→ 4 - 6 = -2 → Negative exponent → move to denominator
✔ Answer: 1/u²
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d) m⁷ / m³
→ 7 - 3 = 4
✔ Answer: m⁴
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e) n² / n⁷
→ 2 - 7 = -5 → Move to denominator
✔ Answer: 1/n⁵
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f) q⁰ / q⁷
→ q⁰ = 1 → So this becomes 1/q⁷
✔ Answer: 1/q⁷
*(Note: You could also do 0 - 7 = -7 → q⁻⁷ = 1/q⁷ — same result)*
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g) e⁹ / e⁶
→ 9 - 6 = 3
✔ Answer: e³
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h) z⁸ / z¹²
→ 8 - 12 = -4 → Move to denominator
✔ Answer: 1/z⁴
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i) m⁴ / m⁹
→ 4 - 9 = -5 → Move to denominator
✔ Answer: 1/m⁵
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j) o¹ / o¹
→ 1 - 1 = 0 → o⁰ = 1
✔ Answer: 1
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k) m¹ / m²
→ 1 - 2 = -1 → Move to denominator
✔ Answer: 1/m
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l) m³ / m³
→ 3 - 3 = 0 → m⁰ = 1
✔ Answer: 1
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m) u⁴ / u¹
→ 4 - 1 = 3
✔ Answer: u³
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n) m⁹ / m³
→ 9 - 3 = 6
✔ Answer: m⁶
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o) k¹⁰ / k⁴
→ 10 - 4 = 6
✔ Answer: k⁶
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##
✔ Final Answers (for quick reference):
a) e⁵
b) 1
c) 1/u²
d) m⁴
e) 1/n⁵
f) 1/q⁷
g) e³
h) 1/z⁴
i) 1/m⁵
j) 1
k) 1/m
l) 1
m) u³
n) m⁶
o) k⁶
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## 💡 Tip:
Always check if you can simplify further — especially watch for exponents that cancel out (like in b, j, l), or become negative (like c, e, h, i, k, f). Remember:
positive exponents only — so convert any negative exponents into fractions.
Let me know if you’d like to practice more or need help with another topic! 😊
Parent Tip: Review the logic above to help your child master the concept of exponent quotient rule worksheet.
