What will come in place of question mark (?) in the following question ?
`((?)^(3.3))/(64) = (512)/((?)^(1.7))`

Options

A. 3
B. 5
C. 4
D. 8

Answer

To solve the equation \(\frac{(?)^{3.3}}{64} = \frac{512}{(?)^{1.7}}\), we will replace the question mark (?) with a variable, let's say \(x\).

### Step-by-Step Solution:

1. **Rewrite the Equation**:
\[ \frac{x^{3.3}}{64} = \frac{512}{x^{1.7}} \]

2. **Cross Multiply**:
To eliminate the fractions, we can cross-multiply:
\[ x^{3.3} \cdot x^{1.7} = 512 \cdot 64 \]

3. **Combine the Exponents**:
When multiplying powers with the same base, we add the exponents:
\[ x^{3.3 + 1.7} = 512 \cdot 64 \]
Simplifying the left side gives:
\[ x^{5} = 512 \cdot 64 \]

4. **Calculate \(512 \cdot 64\)**:
We can calculate \(512 \cdot 64\):
\[ 512 = 2^9 \quad \text{and} \quad 64 = 2^6 \]
Therefore:
\[ 512 \cdot 64 = 2^9 \cdot 2^6 = 2^{9+6} = 2^{15} \]

5. **Set the Equation**:
Now we have:
\[ x^5 = 2^{15} \]

6. **Solve for \(x\)**:
To find \(x\), we take the fifth root of both sides:
\[ x = (2^{15})^{\frac{1}{5}} = 2^{\frac{15}{5}} = 2^3 = 8 \]

Thus, the value that comes in place of the question mark (?) is **8**.