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=an*bn

(1/2)2⋅(x(−1/2))2

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

1/2=1/4

3. Apply the power of a power rule to the variable term, which states that (xa)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/(xn)

1/(4*x)

Final Answer

(1/2*x(−1/2))2=1/(4*x)

Want more problems? Check here!