Calculate (1/3)³: Solving the Cube of One-Third

Question

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

Video Solution

Step-by-Step Solution

To solve the expression (13)3 \left(\frac{1}{3}\right)^3 , we will apply the power of a fraction rule.

Step 1: Begin with the expression (13)3 \left(\frac{1}{3}\right)^3 .
This means we need to calculate 1333 \frac{1^3}{3^3} .

Step 2: Evaluate 13 1^3 and 33 3^3 :
- 13=1×1×1=1 1^3 = 1 \times 1 \times 1 = 1
- 33=3×3×3=27 3^3 = 3 \times 3 \times 3 = 27

Step 3: Construct the fraction with these powers:
1333=127 \frac{1^3}{3^3} = \frac{1}{27} .

Therefore, the value of (13)3 \left(\frac{1}{3}\right)^3 is 127\frac{1}{27}.

Answer

127 \frac{1}{27}