The digit in the unit’s place of the product 71000 3999 is .

GATE 2023 ES – Question 9

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

The digit in the unit’s place of the product $7^{1000} \times 3^{999}$ is _______.

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Correct answer: (A) 7

Explanation

The units digits of powers of 7 repeat as 7, 9, 3, 1, and $1000 = 4 \times 250$, so $7^{1000}$ ends in 1. The units digits of powers of 3 repeat as 3, 9, 7, 1, and $999 = 4 \times 249 + 3$, so $3^{999}$ ends in 7. The product ends in $1 \times 7 = 7$.

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