Solve the followings :
`((x^b)/(x^c))^(a) xx ((x^c)/(x^a))^(b) xx ((x^a)/(x^b))^c` is equal to :

Options

A. 0
B. 1
C. abc
D. None of these

Answer

To solve the expression

\[ \left(\frac{x^b}{x^c}\right)^a \cdot \left(\frac{x^c}{x^a}\right)^b \cdot \left(\frac{x^a}{x^b}\right)^c, \]

we can simplify it step by step.

### Step 1: Simplify each term
We start by simplifying each fraction raised to a power.

1. The first term:
\[ \left(\frac{x^b}{x^c}\right)^a = \frac{x^{b \cdot a}}{x^{c \cdot a}} = x^{ba - ca}. \]

2. The second term:
\[ \left(\frac{x^c}{x^a}\right)^b = \frac{x^{c \cdot b}}{x^{a \cdot b}} = x^{cb - ab}. \]

3. The third term:
\[ \left(\frac{x^a}{x^b}\right)^c = \frac{x^{a \cdot c}}{x^{b \cdot c}} = x^{ac - bc}. \]

### Step 2: Combine the simplified terms
Now we can combine all the simplified terms:

\[ x^{(ba - ca) + (cb - ab) + (ac - bc)}. \]

### Step 3: Simplify the exponent
Next, we simplify the exponent:

\[ (ba - ca) + (cb - ab) + (ac - bc) = ba - ca + cb - ab + ac - bc. \]

Rearranging the terms, we can group them:

\[ = (ba - ab) + (cb - bc) + (ac - ca). \]

Notice that:
- \(ba - ab = 0\) (since multiplication is commutative),
- \(cb - bc = 0\),
- \(ac - ca = 0\).

Thus, the entire exponent simplifies to:

\[ 0. \]

### Step 4: Final result
Therefore, we have:

\[ x^0 = 1. \]

### Conclusion
The value of the original expression is:

\[ \boxed{1}. \]

---