Evaluate the given expression.$\left(\frac{1}{4}\right)^{-1/2}$ | Mathematics MCQ

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Evaluate the given expression. $\left(\frac{1}{4}\right)^{-1/2}$

$\frac{1}{16}$

$2$

$\frac{1}{2}$

$\sqrt{2}$

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option B

$2$

Quick Summary:

For a fraction $(a/b)^{-n/d}$ , invert the fraction to get $(b/a)^{n/d}$ and then compute the root and power. Here, $(1/4)^{-1/2} = (4/1)^{1/2} = \sqrt{4} = 2$ .

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📐MAMath SolutionDirect Formula

📋 Given

Expression to evaluate: (1/4)^(-1/2)

🔢 Formula Used

(x)−n=1xn and (xa)b=xa×b(x)^{-n} = \frac{1}{x^n} \text{ and } (x^a)^b = x^{a \times b}(x)−n=xn1​ and (xa)b=xa×b

⚡ Exam Hall Shortcut / Speed Trick

For a fraction $(a/b)^{-n/d}$ , invert the fraction to get $(b/a)^{n/d}$ and then compute the root and power. Here, $(1/4)^{-1/2} = (4/1)^{1/2} = \sqrt{4} = 2$ .

⚠️ Common Student Trap / Pitfall

Confusing the negative exponent with a negative sign in the result; a negative exponent indicates reciprocal, not negation.

🔢 Step-by-Step Solution

Apply negative exponent rule

The rule for negative exponents states that $x^{-n} = \frac{1}{x^n}$ . Applying this to the expression $(1/4)^{-1/2}$ flips the fraction.

(14)−1/2=(4)1/2(\frac{1}{4})^{-1/2} = (4)^{1/2}(41​)−1/2=(4)1/2

Evaluate the fractional power

An exponent of $1/2$ is equivalent to taking the square root. Therefore, we calculate the square root of 4.

41/2=4=24^{1/2} = \sqrt{4} = 241/2=4​=2

✅

B is correct because the expression evaluates to 2.

Core Concepts Used

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Exponents Reciprocals Square Roots

💡 EXAM TIP

This concept of fractional exponents is foundational in logarithms and radical simplifications, frequently appearing in algebra and calculus sections.

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