4b^5c^3d^3 / 2b^7cd^2

(divided by)

Thanks! ^__^

To simplify the expression (4b^5c^3d^3) / (2b^7cd^2), we can follow these steps:

Step 1: Divide the coefficients (numbers):
The coefficient in the numerator is 4, and the coefficient in the denominator is 2. So, 4 / 2 equals 2.

Step 2: Divide the variables with the same bases:
The base in this expression is b. In the numerator, b is raised to the power of 5, and in the denominator, it is raised to the power of 7. To divide the variables with the same base, we subtract the exponent in the denominator from the exponent in the numerator: 5 - 7 = -2. So, b^-2 can be written as 1 / b^2.

Step 3: Divide the variables with the same base:
The base in this expression is c. In the numerator, c is raised to the power of 3, and in the denominator, there is no c. So, we keep c^3 as it is.

Step 4: Divide the variables with the same base:
The base in this expression is d. In the numerator, d is raised to the power of 3, and in the denominator, it is raised to the power of 2. To divide the variables with the same base, we subtract the exponent in the denominator from the exponent in the numerator: 3 - 2 = 1. So, d^1 can be written as just d.

Putting it all together, the simplified expression is:

2c^3d / b^2

Thus, (4b^5c^3d^3) / (2b^7cd^2) simplifies to 2c^3d / b^2.