Question

For which value of \( n \) is \( (1/2^n)>1 \) true?

• A. \( n = 1/2 \)
• B. \( n = -1/2 \)
• C. \( n = \sqrt{2} \)
• D. \( n = 1 \)

Hint:

To solve inequalities involving exponents, consider the behavior of the base when the exponent is negative or fractional.

Answer 1

The Correct Option is B

Step 1: Analyze the inequality.
We are given the inequality \( \frac{1}{2^n}>1 \), which implies that \( 2^n<1 \).
Step 2: Solve for \( n \).
Since \( 2^n<1 \), it follows that \( n<0 \).
Step 3: Conclusion.
The value \( n = -1/2 \) satisfies the inequality, so the correct answer is \( (B) \).