Final answer:
The result of multiplying the expressions 5a^4b^3 and 8b^2a^3 is 40a^7b^5, after adding the exponents of like bases and multiplying the coefficients together.
Step-by-step explanation:
The result of the expression 5a^4b^3 * 8b^2a^3 is determined by using the properties of exponents. To multiply two exponential expressions with the same base, you add the exponents. Therefore, you add the exponents of a and the exponents of b separately.
For the bases of a, we have a^4 and a^3, so:
a^4 * a^3 = a^(4+3) = a^7
For the bases of b, we have b^3 and b^2, so:
b^3 * b^2 = b^(3+2) = b^5
Multiply the coefficients (the numbers in front of the variables), which are 5 and 8:
5 * 8 = 40
Putting it all together, the final expression is:
40a^7b^5
Thus, the correct answer is A. 40a^7b^5.