Final Answer:
The correct expression, using the product rule of exponents to simplify x³⋅x⁵, is x⁸. (option B)
Step-by-step explanation:
In the context of exponents, the product rule states that when you multiply two exponential expressions with the same base, you add the exponents. For the given expression x³⋅x⁵, both terms have the base x. According to the product rule, you add the exponents, resulting in x⁸.
Now, let's delve into the explanation. When you multiply x³ and x⁵, you are essentially combining the bases (x) and adding their respective exponents (3 and 5). The sum of the exponents gives the power to which the base x is raised in the simplified expression. Therefore, x³⋅x⁵ simplifies to x⁸, adhering to the product rule of exponents.
This application of the product rule is fundamental in handling expressions with the same base, allowing for the concise representation of repeated multiplication. Understanding and correctly applying exponent rules are essential in simplifying algebraic expressions and solving mathematical problems efficiently.(option B)