Let’s solve each problem step by step. We’ll calculate the exponents first, then do the multiplication, division, addition, or subtraction as needed.
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1a. (2/3)² ÷ (1/2)⁶
First, calculate each exponent:
(2/3)² = 2² / 3² = 4/9
(1/2)⁶ = 1⁶ / 2⁶ = 1/64
Now divide:
(4/9) ÷ (1/64) = (4/9) × (64/1) = (4 × 64) / (9 × 1) = 256 / 9
That’s an improper fraction — we can leave it like that or write as mixed number: 28 4/9
But since the worksheet doesn’t specify, we’ll keep it as
256/9
Wait — let me double-check:
Yes, dividing by a fraction means multiplying by its reciprocal. Correct.
✔ Final for 1a:
256/9
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1b. (5/7)² × (5/7)¹
Same base? Yes! So we can add exponents:
(5/7)^(2+1) = (5/7)³ = 125 / 343
Check:
(5/7)² = 25/49
(5/7)¹ = 5/7
Multiply: (25/49) × (5/7) = (25×5)/(49×7) = 125/343 → same!
✔ Final for 1b:
125/343
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2a. 0.6¹ × 0.2³
0.6¹ = 0.6
0.2³ = 0.2 × 0.2 × 0.2 = 0.04 × 0.2 = 0.008
Now multiply:
0.6 × 0.008 = ?
Think: 6 × 8 = 48, and total decimal places: 1 + 3 = 4 → so 0.0048
✔ Final for 2a:
0.0048
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2b. (2/5)³ × (2/5)²
Same base → add exponents: (2/5)^(3+2) = (2/5)^5
Calculate:
2^5 = 32
5^5 = 3125
So: 32/3125
Check:
(2/5)³ = 8/125
(2/5)² = 4/25
Multiply: (8/125) × (4/25) = 32 / 3125 → yes!
✔ Final for 2b:
32/3125
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3a. 1⁹⁹ – 0.6²
1 to any power is still 1 → 1⁹⁹ = 1
0.6² = 0.6 × 0.6 = 0.36
Subtract: 1 – 0.36 = 0.64
✔ Final for 3a:
0.64
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3b. 0.2¹ × (1/8)²
0.2¹ = 0.2
(1/8)² = 1² / 8² = 1/64
Multiply: 0.2 × (1/64)
Convert 0.2 to fraction: 0.2 = 1/5
So: (1/5) × (1/64) = 1/320
Or as decimal: 1 ÷ 320 = 0.003125
Either is fine, but since one part was decimal and one fraction, maybe decimal is okay? But 1/320 is exact.
Let’s go with fraction unless told otherwise.
✔ Final for 3b:
1/320
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4a. (1/2)² ÷ (5/8)¹
(1/2)² = 1/4
(5/8)¹ = 5/8
Divide: (1/4) ÷ (5/8) = (1/4) × (8/5) = (1×8)/(4×5) = 8/20 = 2/5
Simplify: 8÷4=2, 20÷4=5 → 2/5
✔ Final for 4a:
2/5
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4b. 7² – 0.5³
7² = 49
0.5³ = 0.5 × 0.5 × 0.5 = 0.25 × 0.5 = 0.125
Subtract: 49 – 0.125 = 48.875
✔ Final for 4b:
48.875
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5a. 3¹ ÷ 0.8²
3¹ = 3
0.8² = 0.8 × 0.8 = 0.64
Divide: 3 ÷ 0.64
To make easier: 3 ÷ 0.64 = 300 ÷ 64 (multiply numerator and denominator by 100)
300 ÷ 64 = ? Let’s divide:
64 × 4 = 256
300 – 256 = 44 → so 4 and 44/64 = 4 and 11/16
As decimal: 44 ÷ 64 = 0.6875 → so 4.6875
Alternatively: 3 / 0.64 = 300/64 = 75/16 = 4.6875
✔ Final for 5a:
4.6875 or
75/16 — both correct. Since others used decimals sometimes, let’s use decimal here:
4.6875
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5b. 0.7² + 0.9¹
0.7² = 0.49
0.9¹ = 0.9
Add: 0.49 + 0.9 = 1.39
✔ Final for 5b:
1.39
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Final Answer:
1a. 256/9
1b. 125/343
2a. 0.0048
2b. 32/3125
3a. 0.64
3b. 1/320
4a. 2/5
4b. 48.875
5a. 4.6875
5b. 1.39
Parent Tip: Review the logic above to help your child master the concept of exponents math worksheet.
