Simplify (1/2x^(-1/2))^2

Problem

(1/2*x^(−1/2))^2

Solution

1. Apply the power of a product rule, which states that (a*b)^n=a^n*b^n

(1/2)^2⋅(x^(−1/2))^2

2. Evaluate the numerical square by squaring the numerator and the denominator of the fraction.

1^2/2^2=1/4

3. Apply the power of a power rule to the variable term, which states that (x^a)^b=x^(a⋅b)

x^((−1/2)⋅2)=x^(−1)

4. Combine the results into a single expression.

1/4*x^(−1)

5. Rewrite with positive exponents using the rule x^(−n)=1/(x^n)

1/(4*x)

Final Answer

(1/2*x^(−1/2))^2=1/(4*x)

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