What will come in the place of question mark (?) in following questions?
`((8)^(2))/(36) xx (144)/(512) xx 3 (2)/(6)`= ?

Options

A. `(2)/(5)`
B. `(1)/(5)`
C. `(3)/(5)`
D. `(5)/(3)`

Answer

To solve the expression given in the question, we will simplify it step by step. The expression is:

\[ \frac{(8)^2}{36} \times \frac{144}{512} \times \frac{2}{6} \]

### Step 1: Simplify each fraction

First, let's simplify each fraction separately.

1. **Simplifying \(\frac{(8)^2}{36}\)**:
\[ (8)^2 = 64 \]
So, we have:
\[ \frac{64}{36} \]
This can be simplified by dividing both the numerator and the denominator by 4:
\[ \frac{64 \div 4}{36 \div 4} = \frac{16}{9} \]

2. **Simplifying \(\frac{144}{512}\)**:
We can simplify this fraction by finding the greatest common divisor (GCD) of 144 and 512. The GCD is 16:
\[ \frac{144 \div 16}{512 \div 16} = \frac{9}{32} \]

3. **Simplifying \(\frac{2}{6}\)**:
This can also be simplified:
\[ \frac{2 \div 2}{6 \div 2} = \frac{1}{3} \]

### Step 2: Combine the simplified fractions

Now we will combine the simplified fractions:
\[ \frac{16}{9} \times \frac{9}{32} \times \frac{1}{3} \]

### Step 3: Multiply the fractions

We can multiply the numerators and the denominators:
\[ \text{Numerator: } 16 \times 9 \times 1 = 144 \]
\[ \text{Denominator: } 9 \times 32 \times 3 = 864 \]

So, we have:
\[ \frac{144}{864} \]

### Step 4: Simplify the final fraction

Now, we can simplify \(\frac{144}{864}\) by dividing both the numerator and the denominator by 144:
\[ \frac{144 \div 144}{864 \div 144} = \frac{1}{6} \]

### Final Answer

Thus, the value that comes in place of the question mark (?) is:
\[ \frac{1}{6} \]

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