Question

10. Scrieți următoarele numere sub formă de cuburi perfecte: a) 1; 8^2; 125; 27000; 1331; 8000; 15625; b) 2^6, 8^5; 5^12, 7^15; c) 2^2 +2^2; 2^1+5^2, 3 +5^2 +6^2. ​
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Answer 1

a) ○ 1 = 1³

○ 8² = (2³)² = (2²)³

○ 125 = 5³

○ 27 000 = 30³

○ 1 331 = 11³

○ 8 000 = 20³

○ 15 625 = 5^6 = 5^(2*3) = (5²)³

b) ○ 2^6 = 2^(2*3) = (2²)³

○ 8^5 = (2³)^5 = (2^5)³

○ 5^12 = 5^(4*3) = (5^4)³

○ 7^15 = 7^(5*3) = (7^5)³

c) ○ 2² + 2² = 4 + 4 = 8 = 2³

○ 2^1 + 5² = 2 + 25 = 27 = 3³

○ 3 + 5² + 6² = 3 + 25 + 36 = 64 = 4³ = (2²)³