What will come in place of both the question marks ( ? ) in the following questions ?
`((?)^(3//5))/(33) = (3)/((?)^(2//5))`

Options

A. `(99)^2`
B. `sqrt(93)`
C. `3 sqrt(11)`
D. 99

Answer

To solve the equation \(\frac{(?)^{\frac{3}{5}}}{33} = \frac{3}{(?)^{\frac{2}{5}}}\), we will follow these steps:

### Step 1: Substitute the question mark with a variable
Let’s denote the question mark as \(x\). Thus, we rewrite the equation as:
\[ \frac{x^{\frac{3}{5}}}{33} = \frac{3}{x^{\frac{2}{5}}} \]

### Step 2: Cross-multiply the equation
Cross-multiplying gives us:
\[ x^{\frac{3}{5}} \cdot x^{\frac{2}{5}} = 3 \cdot 33 \]

### Step 3: Simplify the right side
Calculating the right side:
\[ 3 \cdot 33 = 99 \]
So we have:
\[ x^{\frac{3}{5}} \cdot x^{\frac{2}{5}} = 99 \]

### Step 4: Combine the powers of \(x\)
Since the bases are the same, we can add the exponents:
\[ x^{\frac{3}{5} + \frac{2}{5}} = 99 \]
This simplifies to:
\[ x^{\frac{5}{5}} = 99 \]
or simply:
\[ x^1 = 99 \]

### Step 5: Solve for \(x\)
Thus, we find:
\[ x = 99 \]

### Conclusion
Both question marks in the original equation can be replaced with \(99\).