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2 la puterea 0 × 2 la puterea 1 × 2 la puterea 2×.... ×2 la puterea 99 × 2 la puterea 1000​

Răspuns :

[tex] {2}^{0} \times {2}^{1} \times {2}^{2} \times ... \times {2}^{99} \times {2}^{1000} = [/tex]

[tex]1 \times {2}^{1 + 2 + ... + 99} \times {2}^{1000} = [/tex]

[tex] {2}^{(99 \times 100) \div 2} \times {2}^{1000} = [/tex]

[tex] {2}^{4950} \times 2 ^{1000} = {2}^{4950 + 1000} [/tex]

[tex] = {2}^{5950} [/tex]