Find the digit in the units place of `(676)^99`.

Options

A. 9
B. 2
C. 4
D. 6

Explanation

To find the digit in the units place of \( (676)^{99} \), we can follow these steps:

### Step 1: Identify the units digit of the base number
The first step is to determine the units digit of the base number, which is 676. The units digit of 676 is 6.

### Step 2: Analyze the pattern of units digits for powers of 6
Next, we need to find the pattern of the units digits when we raise 6 to different powers:
- \( 6^1 = 6 \) (units digit is 6)
- \( 6^2 = 36 \) (units digit is 6)
- \( 6^3 = 216 \) (units digit is 6)
- \( 6^4 = 1296 \) (units digit is 6)

From this, we can observe that the units digit of \( 6^n \) is always 6, regardless of the value of \( n \).

### Step 3: Apply the pattern to the given exponent
Since we need to find the units digit of \( (676)^{99} \), we can replace 676 with its units digit, which is 6. Therefore, we need to find the units digit of \( 6^{99} \).

### Step 4: Conclude the result
Since the units digit of \( 6^n \) is always 6 for any positive integer \( n \), the units digit of \( 6^{99} \) is also 6.

Thus, the units digit of \( (676)^{99} \) is **6**.

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