Find out the unit digit in the -
`(17)^(1999)+(11)^(1999)-(7)^(1999)`

Options

A. 0
B. 1
C. 2
D. 7

Answer

To find the unit digit of the expression \( (17)^{1999} + (11)^{1999} - (7)^{1999} \), we can follow these steps:

### Step 1: Identify the unit digits of the bases
The unit digits of the bases are:
- The unit digit of \( 17 \) is \( 7 \).
- The unit digit of \( 11 \) is \( 1 \).
- The unit digit of \( 7 \) is \( 7 \).

### Step 2: Simplify the expression based on unit digits
We can rewrite the expression using the unit digits:
\[ (17)^{1999} \equiv (7)^{1999} \quad (\text{since we only care about the unit digit}) \]
Thus, we can simplify our expression to:
\[ (7)^{1999} + (1)^{1999} - (7)^{1999} \]

### Step 3: Cancel out the terms
Notice that \( (7)^{1999} \) and \( -(7)^{1999} \) will cancel each other out:
\[ (7)^{1999} - (7)^{1999} = 0 \]
So, we are left with:
\[ 0 + (1)^{1999} = (1)^{1999} \]

### Step 4: Calculate the unit digit of \( (1)^{1999} \)
The unit digit of \( (1)^{1999} \) is simply \( 1 \) because any power of \( 1 \) is \( 1 \).

### Final Result
Thus, the unit digit of the expression \( (17)^{1999} + (11)^{1999} - (7)^{1999} \) is:
\[ \boxed{1} \]