Let’s solve each problem step by step. We’ll calculate the exponents first, then do the addition, subtraction, multiplication, or division as shown.
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1) 5² + 3³
- 5² = 5 × 5 = 25
- 3³ = 3 × 3 × 3 = 27
- 25 + 27 =
52
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2) 99¹ + 10²
- 99¹ = 99 (any number to the power of 1 is itself)
- 10² = 10 × 10 = 100
- 99 + 100 =
199
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3) 2⁶ 4²
- 2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64
- 4² = 4 × 4 = 16
- 64 ÷ 16 =
4
*(Note: You could also notice that 4 = 2², so 4² = (2²)² = 2⁴, and 2⁶ ÷ 2⁴ = 2² = 4 — same answer!)*
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4) 10⁴ + 0¹²
- 10⁴ = 10 × 10 × 10 × 10 = 10,000
- 0¹² = 0 (zero to any positive power is still zero)
- 10,000 + 0 =
10,000
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5) 7² – 20¹
- 7² = 7 × 7 = 49
- 20¹ = 20
- 49 – 20 =
29
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6) 2⁸ – 11²
- 2⁸ = 256 (you can compute: 2⁴=16, 2⁵=32, 2⁶=64, 2⁷=128, 2⁸=256)
- 11² = 11 × 11 = 121
- 256 – 121 =
135
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7) 3² × 2²
- 3² = 9
- 2² = 4
- 9 × 4 =
36
*(Alternatively: (3×2)² = 6² = 36 — same result!)*
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8) 6⁴ ÷ 3⁴
- 6⁴ = 6 × 6 × 6 × 6 = 1296
- 3⁴ = 3 × 3 × 3 × 3 = 81
- 1296 ÷ 81 =
16
*(Or: (6÷3)⁴ = 2⁴ = 16 — faster way!)*
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9) 9³ ÷ 18
- 9³ = 9 × 9 × 9 = 81 × 9 = 729
- 729 ÷ 18 → Let’s divide:
18 × 40 = 720 → 729 - 720 = 9 → so 40 + 9/18 = 40.5
But wait — maybe we can simplify before multiplying?
Better approach:
9³ = (3²)³ = 3⁶
18 = 2 × 3²
So: 3⁶ ÷ (2 × 3²) = 3⁴ ÷ 2 = 81 ÷ 2 =
40.5
But since this is Grade 6, maybe they expect decimal? Or did I misread?
Wait — let me check original: “9³ ÷ 18”
Yes, 729 ÷ 18:
Do long division:
18 into 72 → 4 times (72), remainder 0 → bring down 9 → 18 into 9 → 0.5 → so 40.5
✔ So answer is
40.5
*(If fractions are allowed: 81/2 or 40½)*
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10) 5² × 120¹
- 5² = 25
- 120¹ = 120
- 25 × 120 = ?
Break it down: 25 × 100 = 2500; 25 × 20 = 500 → total = 2500 + 500 =
3000
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11) 0⁷ – 1¹⁵
- 0⁷ = 0
- 1¹⁵ = 1 (one to any power is still one)
- 0 – 1 =
-1
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12) 1¹³ – 9¹
- 1¹³ = 1
- 9¹ = 9
- 1 – 9 =
-8
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Now, compiling all answers in order:
Final Answer:
1) 52
2) 199
3) 4
4) 10000
5) 29
6) 135
7) 36
8) 16
9) 40.5
10) 3000
11) -1
12) -8
Parent Tip: Review the logic above to help your child master the concept of multiplication with exponents worksheet.
