What value will come in place of both question marks (?) in the following question?
`(?)^(4/5)/54 =24/(?)^(6/5)`

Options

A. 18
B. 36
C. 12
D. `-54`

Answer

To solve the equation \((?)^{4/5}/54 = 24/(?)^{6/5}\), we will follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying the equation to eliminate the fractions. This gives us:
\[ (?)^{4/5} \cdot (?)^{6/5} = 24 \cdot 54 \]

### Step 2: Combine the Exponents
Using the property of exponents \(a^m \cdot a^n = a^{m+n}\), we can combine the left side:
\[ (?)^{(4/5 + 6/5)} = 24 \cdot 54 \]
This simplifies to:
\[ (?)^{10/5} = 24 \cdot 54 \]
Which further simplifies to:
\[ (?)^{2} = 24 \cdot 54 \]

### Step 3: Calculate the Right Side
Now we calculate \(24 \cdot 54\):
\[ 24 \cdot 54 = 1296 \]
So we have:
\[ (?)^{2} = 1296 \]

### Step 4: Solve for (?)
To find the value of (?), we take the square root of both sides:
\[ ? = \sqrt{1296} \]

### Step 5: Calculate the Square Root
Now we calculate the square root of 1296:
\[ \sqrt{1296} = 36 \]

### Conclusion
Thus, the value that comes in place of both question marks is:
\[ ? = 36 \]