N is a positive integer. Quantity A: (-1/10)^2N Quantity B: (1/10)(-1)^2N

Rationale

The two quantities are equal.

Both Quantity A and Quantity B simplify to the same expression for any positive integer N. Quantity A, \((-1/10)^{2N}\), results in a positive value since raising a negative number to an even power yields a positive outcome. Quantity B, \((1/10)(-1)^{2N}\), also simplifies to \((1/10) \cdot 1\), which is again positive. Therefore, for any positive integer N, both quantities will always yield the same result.

A (Quantity A is greater.) YOUR ANSWER

This statement is incorrect because both quantities simplify to the same value. Since Quantity A becomes positive and equals Quantity B, it cannot be greater than Quantity B.

B (Quantity B is greater.) YOUR ANSWER

This choice is also incorrect for the same reason as above. Both quantities yield the same positive result, so Quantity B cannot be greater than Quantity A.

C (The two quantities are equal.) CORRECT

This statement is correct as demonstrated; both expressions simplify to the same positive value regardless of the value of N, confirming their equality.

D (The relationship cannot be determined from the information given.) YOUR ANSWER

This choice is incorrect because we can indeed determine the relationship between the two quantities. The simplification shows that both quantities are equal for any positive integer N.

Conclusion

In conclusion, for any positive integer N, the expressions for Quantity A and Quantity B simplify to identical values. Both quantities yield the same positive result, ensuring that they are equal. This equality holds true across all positive integers, making the relationship between them clear and definitive.

N is a positive integer. Quantity A: (-1/10)^2N Quantity B: (1/10)(-1)^2N

The two quantities are equal.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test