Simplify the following :
(i) `11-[7-{5-3(9-3-6)}]`
(ii) `16-[5-2+{7` of `2-(6div3xx2-1+3)}]`.

Answer

Let's simplify the given expressions step by step.

### Part (i): Simplify `11 - [7 - {5 - 3(9 - 3 - 6)}]`

**Step 1:** Start with the innermost bracket: `9 - 3 - 6`.
- Calculation:
\( 9 - 3 = 6 \)
\( 6 - 6 = 0 \)

**Step 2:** Substitute back into the expression:
- The expression now becomes:
\( 11 - [7 - {5 - 3(0)}] \)

**Step 3:** Calculate \( 3(0) \):
- Calculation:
\( 3 \times 0 = 0 \)

**Step 4:** Substitute back into the expression:
- The expression now becomes:
\( 11 - [7 - (5 - 0)] \)

**Step 5:** Calculate \( 5 - 0 \):
- Calculation:
\( 5 - 0 = 5 \)

**Step 6:** Substitute back into the expression:
- The expression now becomes:
\( 11 - [7 - 5] \)

**Step 7:** Calculate \( 7 - 5 \):
- Calculation:
\( 7 - 5 = 2 \)

**Step 8:** Substitute back into the expression:
- The expression now becomes:
\( 11 - 2 \)

**Step 9:** Calculate \( 11 - 2 \):
- Calculation:
\( 11 - 2 = 9 \)

**Final Answer for Part (i):**
The simplified result is **9**.

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### Part (ii): Simplify `16 - [5 - 2 + {7 of 2 - (6 div 3 xx 2 - 1 + 3)}]`

**Step 1:** Start with the innermost bracket: `6 div 3 xx 2 - 1 + 3`.
- First, calculate \( 6 \div 3 \):
\( 6 \div 3 = 2 \)

**Step 2:** Substitute back into the expression:
- The expression now becomes:
\( 16 - [5 - 2 + {7 \times 2 - (2 \times 2 - 1 + 3)}] \)

**Step 3:** Calculate \( 2 \times 2 \):
- Calculation:
\( 2 \times 2 = 4 \)

**Step 4:** Substitute back into the expression:
- The expression now becomes:
\( 16 - [5 - 2 + {7 \times 2 - (4 - 1 + 3)}] \)

**Step 5:** Calculate \( 4 - 1 + 3 \):
- Calculation:
\( 4 - 1 = 3 \)
\( 3 + 3 = 6 \)

**Step 6:** Substitute back into the expression:
- The expression now becomes:
\( 16 - [5 - 2 + {7 \times 2 - 6}] \)

**Step 7:** Calculate \( 7 \times 2 \):
- Calculation:
\( 7 \times 2 = 14 \)

**Step 8:** Substitute back into the expression:
- The expression now becomes:
\( 16 - [5 - 2 + (14 - 6)] \)

**Step 9:** Calculate \( 14 - 6 \):
- Calculation:
\( 14 - 6 = 8 \)

**Step 10:** Substitute back into the expression:
- The expression now becomes:
\( 16 - [5 - 2 + 8] \)

**Step 11:** Calculate \( 5 - 2 + 8 \):
- Calculation:
\( 5 - 2 = 3 \)
\( 3 + 8 = 11 \)

**Step 12:** Substitute back into the expression:
- The expression now becomes:
\( 16 - 11 \)

**Step 13:** Calculate \( 16 - 11 \):
- Calculation:
\( 16 - 11 = 5 \)

**Final Answer for Part (ii):**
The simplified result is **5**.

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