x = 2, a = 1, b = 2 এবং c = 3 হলে[( x^a+b)^2×(x^b+c)^2×(x^c+a)^2]/x^a×x^b×x^c

To solve the expression given the values \( x = 2 \), \( a = 1 \), \( b = 2 \), and \( c = 3 \), we first substitute these values into the expression:

\[
\frac{[(x^a + b)^2 \times (x^b + c)^2 \times (x^c + a)^2]}{x^a \times x^b \times x^c}
\]

### Step-by-step Solution:

1. **Substitute the values of \( x \), \( a \), \( b \), and \( c \):**

   - \( x = 2 \)
   - \( a = 1 \)
   - \( b = 2 \)
   - \( c = 3 \)

   Plugging these into the expression, we get:

   \[
   \frac{[(2^1 + 2)^2 \times (2^2 + 3)^2 \times (2^3 + 1)^2]}{2^1 \times 2^2 \times 2^3}
   \]

2. **Calculate the powers of 2 and simplify each term:**

   - \( 2^1 = 2 \)
   - \( 2^2 = 4 \)
   - \( 2^3 = 8 \)

   Now, substitute these values into the expression:

   \[
   \frac{[(2 + 2)^2 \times (4 + 3)^2 \times (8 + 1)^2]}{2 \times 4 \times 8}
   \]

3. **Simplify the terms inside the parentheses:**

   - \( 2 + 2 = 4 \)
   - \( 4 + 3 = 7 \)
   - \( 8 + 1 = 9 \)

   So, the expression becomes:

   \[
   \frac{[4^2 \times 7^2 \times 9^2]}{2 \times 4 \times 8}
   \]

4. **Calculate the squares:**

   - \( 4^2 = 16 \)
   - \( 7^2 = 49 \)
   - \( 9^2 = 81 \)

   Substitute these into the expression:

   \[
   \frac{16 \times 49 \times 81}{2 \times 4 \times 8}
   \]

5. **Calculate the denominator:**

   - \( 2 \times 4 = 8 \)
   - \( 8 \times 8 = 64 \)

   So, the expression is:

   \[
   \frac{16 \times 49 \times 81}{64}
   \]

6. **Calculate the numerator:**

   - \( 16 \times 49 = 784 \)
   - \( 784 \times 81 = 63456 \)

   Thus, the fraction simplifies to:

   \[
   \frac{63456}{64}
   \]

7. **Simplify the fraction:**

   Divide the numerator by the denominator:

   \[
   \frac{63456}{64} = 992
   \]

### Final Answer:

The value of the expression is **992**.

---

Do you have any questions or would you like further clarification on this solution?

### Relative Questions:

1. How would the result change if \( x \) were a different value?
2. What if we changed the powers \( a \), \( b \), or \( c \) to different values?
3. How can this expression be simplified without evaluating each step numerically?
4. What mathematical properties are useful in simplifying such expressions?
5. How does the choice of base affect the simplification process?

**Tip:** When working with exponents, always simplify step by step to avoid mistakes in calculations.

Learn how to solve the expression [(2^1 + 2)^2 × (2^2 + 3)^2 × (2^3 + 1)^2] / (2^1 × 2^2 × 2^3) with a detailed step-by-step solution. This problem involves exponents and algebraic manipulation. Suitable for students in Grades 9-12.

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