Calculate (1/3)² : Finding the Square of One-Third

Question

(13)2= (\frac{1}{3})^2=

Video Solution

Step-by-Step Solution

To solve for (13)2 \left( \frac{1}{3} \right)^2 , we follow these steps:

  • Step 1: Identify the given fraction, which is 13 \frac{1}{3} .
  • Step 2: Apply the formula for squaring a fraction: (ab)2=a2b2 \left( \frac{a}{b} \right)^2 = \frac{a^2}{b^2} .
  • Step 3: Square the numerator: 12=1 1^2 = 1 .
  • Step 4: Square the denominator: 32=9 3^2 = 9 .
  • Step 5: Form the new fraction using the squared values: 1232=19 \frac{1^2}{3^2} = \frac{1}{9} .

Therefore, the solution to (13)2 \left( \frac{1}{3} \right)^2 is 19 \frac{1}{9} .

Answer

19 \frac{1}{9}