`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 given equation:
\[ \frac{\sqrt[3]{x}}{2.56} = \frac{100}{x} \]
Cross-multiplying gives us:
\[ \sqrt[3]{x} \cdot x = 100 \cdot 2.56 \]

### Step 2: Simplify the left side
The left side can be rewritten using the property of exponents:
\[ \sqrt[3]{x} = x^{1/3} \]
Thus, we have:
\[ x^{1/3} \cdot x = x^{1/3 + 1} = x^{4/3} \]
So the equation now looks like:
\[ x^{4/3} = 100 \cdot 2.56 \]

### Step 3: Calculate the right side
Now we calculate \(100 \cdot 2.56\):
\[ 100 \cdot 2.56 = 256 \]
So we now have:
\[ x^{4/3} = 256 \]

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

### Step 5: Simplify \(256^{3/4}\)
First, we express \(256\) as a power of \(2\):
\[ 256 = 2^8 \]
Now substituting this into our equation:
\[ x = (2^8)^{3/4} \]
Using the property of exponents, we multiply the exponents:
\[ x = 2^{8 \cdot \frac{3}{4}} = 2^{6} = 64 \]

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