$(\frac{1}{2})^{-\frac{1}{2}}$ is equal to

### Concept & Formula This question assesses the direct application of negative and fractional exponents. A negative exponent flips the base (takes the reciprocal), and a fractional exponent of $1/2$ is equivalent to a square root. $$ (\frac{a}{b})^{-n} = (\frac{b}{a})^n $$ $$ x^{\frac{1}{2}} = \sqrt{x} $$ ### Step-by-Step Solution * **Given:** The expression to evaluate is $(\frac{1}{2})^{-\frac{1}{2}}$. * **Calculation:** 1. Apply the negative exponent rule. To make the exponent positive, flip the fraction inside the parentheses: $(\frac{2}{1})^{\frac{1}{2}}$ 2. Simplify the base: $2^{\frac{1}{2}}$ 3. Convert the fractional exponent into its radical form: $\sqrt{2}$ ### Exam Strategy & Shortcut This problem should be solved purely mentally in 2 seconds. You see a negative power over a fraction; immediately flip the fraction ($1/2$ becomes $2$). You see a power of $1/2$; immediately apply a square root. The result is instantly $\sqrt{2}$. No intermediate written steps are required. ### Common Pitfall A very frequent mistake is assuming that a negative exponent will result in a negative final answer, leading students to incorrectly choose option (c) $-\sqrt{2}$. Exponents dictate repeated multiplication or reciprocals, not the positive/negative sign of the base. ### Final Answer **Therefore, the correct answer is $\sqrt{2}$.**