Answer
The pair is not equivalent
Work Step by Step
This problem deals with combining like terms. Like terms are terms that have the same variable raised to the same power. Note, by this definition, numbers like 10 and 15 are also like terms as they are multiplied by a variable raised to the zeroth power. This concept may seem confusing, but it makes sense if we consider it for a second. Anything raised to the zeroth power is one. Thus, $x^{0}$ is 1. Earlier in the chapter, we learned the Identity Property of Multiplication, which states that anything times one is itself. Thus, 15 is equal to 15$x^{0}$ because $x^{0}$ is equal to 1.
Now, back to the problem. Recall, if terms are like terms, we can add or subtract these terms just like we add or subtract numbers. Thus, because 41 and 9 are like terms, we can add them to simplify the expression to z+50.
Now, to the second expression. The Commutative Property of Multiplication states that the order in which multiple things are multiplied does not matter. Thus, we can multiply 41 and 9 to get a final expression of 369z.
369z does not equal z+50, so the pair is not equivalent.
