Final answer:
To calculate the product of (1/2a^2b^5)*(3/8a^4bc^2), multiply the coefficients to get 3/16, add the exponents of like bases to get a^6 and b^6, and retain c^2, resulting in (3/16)a^6b^6c^2.
Step-by-step explanation:
To find the product of the monomials (1/2a^2b^5) and (3/8a^4bc^2), we will use the rule that when we multiply two powers with the same base, we add the exponents.
Also, we multiply the coefficients as we would with any other numbers.
The product of the coefficients (1/2) and (3/8) is (1/2) * (3/8) = 3/16.
For the variable a, we add the exponents: a^2 * a^4 = a^(2+4) = a^6.
For the variable b, we do the same: b^5 * b = b^(5+1) = b^6.
And for the variable c, since it only appears in the second monomial with an exponent of 2, it remains c^2.
Therefore, the product of these two monomials is (3/16)a^6b^6c^2.