To understand the equation x = a^2 / b^2 * (a*b) and explain it in detail, we need to break it down into its components and analyze each part separately.

1. Understanding the Equation:
The given equation x = a^2 / b^2 * (a*b) can be simplified using the order of operations (PEMDAS/BODMAS) as follows:
1. First, we calculate the square of 'a' by multiplying it with itself, denoted as a^2.
2. Then, we calculate the square of 'b' by multiplying it with itself, denoted as b^2.
3. Next, we divide a^2 by b^2, which gives us the result of a^2 / b^2.
4. Finally, we multiply the result of a^2 / b^2 by (a*b).

2. Breaking Down the Equation:

a. Square of 'a' (a^2):
When we square a number, we multiply it by itself. In this equation, 'a' is squared by multiplying it with itself, denoted as a^2.

b. Square of 'b' (b^2):
Similarly, 'b' is squared by multiplying it with itself, denoted as b^2.

c. Division of a^2 by b^2 (a^2 / b^2):
After calculating the squares of a and b, we divide a^2 by b^2. This division operation results in the division of the square of 'a' by the square of 'b'.

d. Multiplication of a^2 / b^2 by (a*b):
Finally, we multiply the result of a^2 / b^2 by (a*b). This multiplication operation involves multiplying the division result with the product of 'a' and 'b'.

3. Simplifying the Equation:
To simplify the equation further, we can combine the operations and rewrite it as x = (a^2 * a * b) / b^2. This expression demonstrates that the numerator consists of a^2 multiplied by a and b, while the denominator remains as b^2.

4. Conclusion:
In conclusion, the equation x = a^2 / b^2 * (a*b) involves squaring 'a' and 'b', dividing the square of 'a' by the square of 'b', and multiplying the division result by the product of 'a' and 'b'. It represents a mathematical relationship between these variables and can be further simplified by combining the operations.