What is the units digit of 2^{2047} imes 3^{11}?

Question

What is the units digit of 2^{2047} 	imes 3^{11}?

Accepted Answer

{"content":[{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 1 (Units digit of 2^2047):"},{"type":"text","text":" The units digit of powers of 2 cycle with period 4: "},{"attrs":{"latex":"\{2, 4, 8, 6\}"},"type":"math_inline"},{"text":".","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"2047 = 4 \times 511 + 3 \implies 2^{2047} \equiv 2^3 \equiv 8 \pmod{10}"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Units digit of 3^11):","type":"text"},{"type":"text","text":" The units digit of powers of 3 cycle with period 4: "},{"attrs":{"latex":"\{3, 9, 7, 1\}"},"type":"math_inline"},{"text":".","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"11 = 4 \times 2 + 3 \implies 3^{11} \equiv 3^3 \equiv 7 \pmod{10}"},"type":"math_block"},{"content":[{"text":"Step 3 (Product Units Digit):","type":"text","marks":[{"type":"bold"}]}],"type":"paragraph"},{"attrs":{"latex":"\text{Product units digit} \equiv 8 \times 7 = 56 \equiv 6 \pmod{10}"},"type":"math_block"},{"content":[{"text":"Step 4 (Conclusion):","type":"text","marks":[{"type":"bold"}]},{"text":" The units digit is 6, which is at option index ","type":"text"},{"text":"2","type":"text","marks":[{"type":"code"}]},{"type":"text","text":" in "},{"marks":[{"type":"code"}],"text":"['2', '4', '6', '8']","type":"text"},{"text":".","type":"text"}],"type":"paragraph"}],"type":"doc"}

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