Let’s solve each problem one by one. We’ll use exponent rules:
- When multiplying same base: add exponents → a^m × a^n = a^(m+n)
- When dividing same base: subtract exponents → a^m ÷ a^n = a^(m−n)
- When raising a power to another power: multiply exponents → (a^m)^n = a^(m×n)
- Also, remember that coefficients are multiplied or divided normally.
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Problem 1:
7s⁴ / 3s
→ Coefficients: 7/3 stays as is
→ s⁴ / s¹ = s^(4−1) = s³
✔ Final:
(7/3)s³
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Problem 2:
(1/s)⁶ × (1/s)² × (1/s)⁴
→ All have same base: 1/s
→ Add exponents: 6 + 2 + 4 = 12
→ So: (1/s)¹² = 1/s¹²
✔ Final:
1/s¹²
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Problem 3:
(4cb⁵)⁵
→ Apply exponent to each part inside parentheses:
4⁵ × c⁵ × (b⁵)⁵
→ 4⁵ = 1024
→ (b⁵)⁵ = b^(5×5) = b²⁵
✔ Final:
1024c b²⁵
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Problem 4:
9cy⁷ / 5c³y³
→ Coefficients: 9/5
→ c¹ / c³ = c^(1−3) = c⁻² → write as 1/c²
→ y⁷ / y³ = y^(7−3) = y⁴
So: (9/5) × (y⁴ / c²)
✔ Final:
(9y⁴)/(5c²)
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Problem 5:
(br / 3b²r)²
First simplify inside:
b¹ / b² = b⁻¹ → 1/b
r¹ / r¹ = r⁰ = 1
So inside becomes: (1 / 3b)
Now square it: (1/(3b))² = 1² / (3² × b²) = 1/(9b²)
✔ Final:
1/(9b²)
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Problem 6:
(2c² / 6c)³
Simplify inside first:
2/6 = 1/3
c² / c¹ = c¹
So inside: (1/3)c → or c/3
Now cube it: (c/3)³ = c³ / 27
✔ Final:
c³/27
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Problem 7:
(2c × 3c³ × c²)²
Multiply inside first:
Coefficients: 2 × 3 = 6
c¹ × c³ × c² = c^(1+3+2) = c⁶
Inside: 6c⁶
Now square it: (6c⁶)² = 6² × (c⁶)² = 36c¹²
✔ Final:
36c¹²
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Problem 8:
6g² × 4g⁴t⁵
Coefficients: 6 × 4 = 24
g² × g⁴ = g⁶
t⁵ stays
✔ Final:
24g⁶t⁵
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Problem 9:
(7g⁹n⁷ / 3gn²)²
Simplify inside first:
7/3 stays
g⁹ / g¹ = g⁸
n⁷ / n² = n⁵
Inside: (7/3)g⁸n⁵
Now square: (7/3)² × (g⁸)² × (n⁵)² = 49/9 × g¹⁶ × n¹⁰
✔ Final:
(49g¹⁶n¹⁰)/9
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Problem 10:
8k × 6k⁻³
Coefficients: 8 × 6 = 48
k¹ × k⁻³ = k^(1−3) = k⁻² → 1/k²
✔ Final:
48/k²
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Problem 11:
3g⁴ / 4g³
Coefficients: 3/4
g⁴ / g³ = g¹
✔ Final:
(3g)/4
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Problem 12:
(5y⁴z)⁴
Apply exponent to each part:
5⁴ = 625
(y⁴)⁴ = y¹⁶
z⁴ = z⁴
✔ Final:
625y¹⁶z⁴
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Final Answer:
1) $\frac{7}{3}s^3$
2) $\frac{1}{s^{12}}$
3) $1024cb^{25}$
4) $\frac{9y^4}{5c^2}$
5) $\frac{1}{9b^2}$
6) $\frac{c^3}{27}$
7) $36c^{12}$
8) $24g^6t^5$
9) $\frac{49g^{16}n^{10}}{9}$
10) $\frac{48}{k^2}$
11) $\frac{3g}{4}$
12) $625y^{16}z^4$
Parent Tip: Review the logic above to help your child master the concept of printable basic exponent worksheet.
