The value of `17-[16-{38-(49-72div16xx4`of 2)}] is :

Options

A. 23
B. 29
C. 28
D. 26

Answer

To solve the expression \( 17 - [16 - \{38 - (49 - 72 \div 16 \times 4 \text{ of } 2)\}]\), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step-by-step Solution:

1. **Identify the innermost operation**:
Start with the innermost expression: \( 72 \div 16 \times 4 \text{ of } 2 \).

- First, perform the division:
\[ 72 \div 16 = 4.5 \]

- Now, multiply \( 4.5 \) by \( 4 \):
\[ 4.5 \times 4 = 18 \]

- Then, multiply \( 18 \) by \( 2 \):
\[ 18 \text{ of } 2 = 36 \]

2. **Substitute back into the expression**:
Replace \( 49 - 72 \div 16 \times 4 \text{ of } 2 \) with \( 49 - 36 \):
\[ 49 - 36 = 13 \]

3. **Continue simplifying**:
Now substitute back into the expression:
\[ 17 - [16 - \{38 - 13\}] \]
Calculate \( 38 - 13 \):
\[ 38 - 13 = 25 \]

4. **Substitute again**:
Now we have:
\[ 17 - [16 - 25] \]
Calculate \( 16 - 25 \):
\[ 16 - 25 = -9 \]

5. **Final calculation**:
Now substitute back:
\[ 17 - (-9) = 17 + 9 = 26 \]

Thus, the final value of the expression is \( \boxed{26} \).