Evaluate the following after simplifying the multiplication using properties of multiplication.
`(-59) times (-103)`

Answer

To evaluate the expression \((-59) \times (-103)\), we can simplify it using the properties of multiplication. Here’s a step-by-step solution:

### Step 1: Rewrite the expression
We start with the expression:
\[ (-59) \times (-103) \]
We can rewrite \(-103\) as \(-100 - 3\):
\[ (-59) \times (-103) = (-59) \times (-100 - 3) \]

### Step 2: Apply the distributive property
Using the distributive property of multiplication, we can expand the expression:
\[ (-59) \times (-100 - 3) = (-59) \times (-100) + (-59) \times (-3) \]

### Step 3: Multiply the terms
Now we calculate each term separately:
1. For \((-59) \times (-100)\):
\[ (-59) \times (-100) = 59 \times 100 = 5900 \]
(Since the product of two negative numbers is positive.)

2. For \((-59) \times (-3)\):
\[ (-59) \times (-3) = 59 \times 3 = 177 \]
(Again, the product of two negative numbers is positive.)

### Step 4: Add the results
Now we add the two results together:
\[ 5900 + 177 = 6077 \]

### Final Answer
Thus, the value of \((-59) \times (-103)\) is:
\[ \boxed{6077} \]

---