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What is the unit digit of (2) ^29 * (5) ^29 * (7) ^29?

Q) What is the unit digit of (2) ^29 * (5) ^29 * (7) ^29?

A) 1
B) 5
c) 9
D) 0
E) 7

To answer questions that involve multiplying large numbers and finding the unit digit, the solution is to find patterns within numbers. In this case, each number is raised to the 29th power and multiplied with each number. All numbers that are raised to a certain power follows a pattern. Let us look at each of them.

(2)^29    
(2)^1 = 2
(2)^2 = 4
(2)^3 = 8
(2)^4 = 16
(2)^5 = 32


The power of 2 has unit digit in the following pattern (2,4,8,6)

Unit Digit of (2)^29 = 2  -> First Statement

We know that Unit Digit (5)^29 = 5 -> Second Statement

Unit Digits For (7)^29 has the following pattern

(7)^1 = 7
(7)^2 = 9
(7)^3 = 3
(7)^4 = 1
(2)^5 = 7


The power of 7 has unit digit in the following pattern (7,9,3,1)

Unit Digit of (7)^29 = 7 -> Statement 3

Unit Digit obtained by multiplying Statements 1, 2 and 3, we get 2 x 5 x 7 is 0

Correct Answer: D

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