`root(3)(x)/2.56=100/x`, then 'x' is equal to:

Options

A. 4
B. 16
C. 64
D. 256

Answer

To solve the equation \( \frac{\sqrt[3]{x}}{2.56} = \frac{100}{x} \), we will follow these steps:

### Step 1: Cross-multiply the equation
We start with the equation:
\[ \frac{\sqrt[3]{x}}{2.56} = \frac{100}{x} \]
Cross-multiplying gives us:
\[ \sqrt[3]{x} \cdot x = 100 \cdot 2.56 \]
This simplifies to:
\[ x^{1 + \frac{1}{3}} = 256 \]

### Step 2: Simplify the exponent
The exponent \( 1 + \frac{1}{3} \) can be expressed as:
\[ x^{\frac{3}{3} + \frac{1}{3}} = x^{\frac{4}{3}} \]
Thus, we rewrite the equation as:
\[ x^{\frac{4}{3}} = 256 \]

### Step 3: Solve for \( x \)
To isolate \( x \), we raise both sides to the power of \( \frac{3}{4} \):
\[ x = 256^{\frac{3}{4}} \]

### Step 4: Calculate \( 256^{\frac{3}{4}} \)
First, we find \( 256^{\frac{1}{4}} \):
\[ 256 = 4^4 \quad \text{(since } 4^4 = 256\text{)} \]
Thus,
\[ 256^{\frac{1}{4}} = 4 \]
Now we raise this to the power of 3:
\[ x = 4^3 = 64 \]

### Final Answer
The value of \( x \) is:
\[ \boxed{64} \]