The value of `(5^((1)/(4))-: (3)/(7)"of"(1)/(2)) -: (5(1)/(9)-7(7)/(8)-: 9 (9)/(20)) xx(11)/(21)+ (2-: 2 "of" (1)/(2)) ` is :

Options

A. `(9)/(4)`
B. 5
C. 3
D. `(7)/(2)`

Answer

To solve the expression \((5^{(1/4)} \div (3/7) \text{ of } (1/2)) \div (5^{(1/9)} - 7^{(7/8)} \div 9^{(9/20)}) \times (11/21) + (2 \div 2 \text{ of } (1/2))\), we will follow these steps:

### Step 1: Simplify the components
- Convert \(5^{(1/4)}\) to a fraction:
\[ 5^{(1/4)} = \frac{21}{4} \quad \text{(since } 5 \times 4 = 20 + 1 = 21\text{)} \]

### Step 2: Calculate \(3/7 \text{ of } (1/2)\)
- The term \((3/7) \text{ of } (1/2)\) means multiplying:
\[ (3/7) \times (1/2) = \frac{3}{14} \]

### Step 3: Calculate the first part of the expression
- Now we have:
\[ \frac{21}{4} \div \frac{3}{14} \]
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{21}{4} \times \frac{14}{3} = \frac{21 \times 14}{4 \times 3} = \frac{294}{12} = \frac{49}{2} \quad \text{(after simplification)} \]

### Step 4: Simplify the second part of the expression
- Calculate \(5^{(1/9)}\):
\[ 5^{(1/9)} = \frac{46}{9} \quad \text{(since } 5 \times 9 = 45 + 1 = 46\text{)} \]
- Calculate \(7^{(7/8)}\):
\[ 7^{(7/8)} = \frac{63}{8} \quad \text{(since } 7 \times 8 = 56 + 7 = 63\text{)} \]
- Calculate \(9^{(9/20)}\):
\[ 9^{(9/20)} = \frac{189}{20} \quad \text{(since } 9 \times 20 = 180 + 9 = 189\text{)} \]
- Now compute:
\[ \frac{63}{8} \div \frac{189}{20} = \frac{63}{8} \times \frac{20}{189} = \frac{1260}{1512} = \frac{5}{6} \quad \text{(after simplification)} \]

### Step 5: Combine the results
- Now we have:
\[ \frac{49}{2} \div \left(\frac{46}{9} - \frac{5}{6}\right) \]
- Find a common denominator for \(\frac{46}{9}\) and \(\frac{5}{6}\):
\[ \text{LCM of 9 and 6 is 18.} \]
- Convert:
\[ \frac{46}{9} = \frac{92}{18}, \quad \frac{5}{6} = \frac{15}{18} \]
- Subtract:
\[ \frac{92}{18} - \frac{15}{18} = \frac{77}{18} \]

### Step 6: Final calculation
- Now we compute:
\[ \frac{49}{2} \div \frac{77}{18} = \frac{49}{2} \times \frac{18}{77} = \frac{882}{154} = \frac{63}{11} \quad \text{(after simplification)} \]
- Multiply by \(\frac{11}{21}\):
\[ \frac{63}{11} \times \frac{11}{21} = \frac{63}{21} = 3 \]

### Step 7: Add the last part
- Calculate \(2 \div 2 \text{ of } (1/2)\):
\[ 2 \div 1 = 2 \]
- Finally, add:
\[ 3 + 2 = 5 \]

### Final Answer
The value of the expression is \(5\).