Square of a Fraction Problem: Simplifying (1/2)²

Question

(12)2= (\frac{1}{2})^2=

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the fraction to be squared, which is 12\frac{1}{2}.
  • Step 2: Apply the exponent rule for fractions.
  • Step 3: Calculate the result by squaring both the numerator and denominator.

Now, let's work through each step:
Step 1: We have the fraction 12\frac{1}{2}.
Step 2: When squaring a fraction, apply the formula (ab)n=anbn(\frac{a}{b})^n = \frac{a^n}{b^n}.
Step 3: Using (12)2=1222(\frac{1}{2})^2 = \frac{1^2}{2^2}, we calculate
- The square of the numerator is 12=11^2 = 1.
- The square of the denominator is 22=42^2 = 4.
- Therefore, (12)2=14(\frac{1}{2})^2 = \frac{1}{4}.

Thus, the solution to the problem is 14\frac{1}{4}.

Answer

14 \frac{1}{4}