Final answer:
The expression (5ab⁴c)(-abc²) simplifies to -5a²b⁵c³ by multiplying coefficients and adding the exponents of the same base variables.
Step-by-step explanation:
The question asks us to simplify the expression (5ab⁴c)(-abc²). To do this, we will apply the rules of exponents and the properties of multiplication.
First, we multiply the coefficients (numerical part) of the terms: 5 multiplied by -1 (the coefficient of abc² is inherently -1). This gives us -5.
Next, we consider the variable 'a'. There is one 'a' in each term, so we add the exponents (which are both 1 in this case), resulting in a².
For the variable 'b', we have b⁴ in the first term and b in the second term. Again, we add the exponents, 4 + 1, which gives b⁵.
Lastly, for the variable 'c', we have c in the first term and c² in the second term. Adding the exponents (1 + 2) yields c³.
By combining all these results, our simplified expression is -5a²b⁵c³.
This answer corresponds to choice A, which is -5a²b⁵c³. It is important to remember that when you multiply variables that have the same base, you add their exponents.