Final answer:
To find the LCM of the two radical expressions, 7/(10x²y) and 4/(15xy²), simplify each expression and find the LCM of each term. The LCM is 2/(3x²y²).
Step-by-step explanation:
To find the least common multiple (LCM) of the two radical expressions, 7/(10x²y) and 4/(15xy²), we need to simplify each expression first.
The first expression can be simplified as follows:
- 7/(10x²y) = (7/10) * (1/x²) * (1/y)
The second expression can be simplified as:
- 4/(15xy²) = (4/15) * (1/x) * (1/y²)
Now, we need to find the LCM of all the terms in both expressions.
The LCM of (7/10) and (4/15) is 2/3.
The LCM of (1/x²) and (1/x) is (1/x²).
The LCM of (1/y) and (1/y²) is (1/y²).
Therefore, the LCM of the two expressions is (2/3) * (1/x²) * (1/y²), which can be written as 2/(3x²y²).