Final answer:
The correct statement showing that 2x + 3x² is not the same as 5x³ is b) 2x + 3x² ≠ 5x³. These terms, with different exponents, cannot simply be added together to form a new term with a summed exponent.
Step-by-step explanation:
Frank thinks that 2x + 3x² is the same as 5x³. The statement that shows these expressions are not the same is b) 2x + 3x² ≠ 5x³. Algebraic expressions must follow the law of exponents and cannot be combined unless they have the same bases and exponents. The terms 2x and 3x² cannot be combined to make 5x³ because they don't have the same exponent. For instance, when multiplying numbers with the same base, we add their exponents; for example, 5± × 5± becomes 5², which is 25, not 5. When facing different powers of the same variable, such as in 2x and 3x², they remain separate terms as the exponents differ.