What is the units digit of `16^(4)xx27^(3)`?

Answer

To find the units digit of \( 16^4 \times 27^3 \), we can follow these steps:

### Step 1: Identify the units digits of the base numbers
The units digit of \( 16 \) is \( 6 \) and the units digit of \( 27 \) is \( 7 \).

### Step 2: Calculate the units digit of \( 16^4 \)
Since we only need the units digit, we can focus on \( 6^4 \):
- \( 6^1 = 6 \) (units digit is \( 6 \))
- \( 6^2 = 36 \) (units digit is \( 6 \))
- \( 6^3 = 216 \) (units digit is \( 6 \))
- \( 6^4 = 1296 \) (units digit is \( 6 \))

Thus, the units digit of \( 16^4 \) is \( 6 \).

### Step 3: Calculate the units digit of \( 27^3 \)
Now we calculate the units digit of \( 7^3 \):
- \( 7^1 = 7 \) (units digit is \( 7 \))
- \( 7^2 = 49 \) (units digit is \( 9 \))
- \( 7^3 = 343 \) (units digit is \( 3 \))

Thus, the units digit of \( 27^3 \) is \( 3 \).

### Step 4: Multiply the units digits
Now we multiply the units digits we found:
- Units digit of \( 16^4 \) is \( 6 \)
- Units digit of \( 27^3 \) is \( 3 \)

Now, calculate \( 6 \times 3 = 18 \). The units digit of \( 18 \) is \( 8 \).

### Final Answer
Therefore, the units digit of \( 16^4 \times 27^3 \) is \( 8 \).

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