Ratio of cube sums when every term is scaled by k: 1/k^3

This type of question, asked 7 times: 14 Sep 2025 S1, 16 Sep 2025 S2, 17 Sep 2025 S2, 18 Sep 2025 S1, 18 Sep 2025 S2, 18 Sep 2025 S3, 19 Sep 2025 S3. All 10 questions below, oldest first.

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Question 1
14 Sep 2025 S1
52 $\frac{(0.1 \times 0.1 \times 0.1 + 0.03 \times 0.03 \times 0.03)}{(0.3 \times 0.3 \times 0.3 + 0.09 \times 0.09 \times 0.09)}$
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Question 2
16 Sep 2025 S2
75 $(0.05^3 + 0.01^3) \div (0.25^3 + 0.05^3)$
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Question 3
17 Sep 2025 S2
74 $(0.02^3 + 0.004^3) \div (0.2^3 + 0.04^3)$
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Question 4
17 Sep 2025 S2
75 $(0.4 \times 0.4 \times 0.4 + 0.02 \times 0.02 \times 0.02) \div (1.2 \times 1.2 \times 1.2 + 0.06 \times 0.06 \times 0.06)$
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Question 5
18 Sep 2025 S1
75 $\left((0.5)^3 + (0.05)^3 + (0.005)^3\right) \div \left((0.1)^3 + (0.01)^3 + (0.001)^3\right)$
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Question 6
18 Sep 2025 S1
74 $(0.12^3 + 0.06^3) \div (0.24^3 + 0.12^3)$
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Question 7
18 Sep 2025 S2
75 $(0.04^3 + 0.02^3) \div (0.2^3 + 0.1^3)$
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Question 8
18 Sep 2025 S3
74 $(0.25^3 + 0.05^3) \div (0.5^3 + 0.1^3)$
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Question 9
18 Sep 2025 S3
75 $(0.05^3 + 0.005^3) \div (0.25^3 + 0.025^3)$
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Question 10
19 Sep 2025 S3
75 $(0.2^3 + 0.02^3) \div (0.4^3 + 0.04^3)$
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Ratio of cube sums when every term is scaled by k: 1/k^3

Question 1

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Question 5

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Question 10