Sure, let's evaluate the expression step-by-step:
We are given the expression:
[tex]\[ \left(2 - \frac{1}{3}\right)^3 \][/tex]
### Step 1: Simplify the base
First, we need to simplify the expression inside the parentheses:
[tex]\[ 2 - \frac{1}{3} \][/tex]
To perform the subtraction, we find a common denominator for the fractions. Here, 2 can be written as:
[tex]\[ 2 = \frac{6}{3} \][/tex]
Now, we subtract:
[tex]\[ \frac{6}{3} - \frac{1}{3} = \frac{6 - 1}{3} = \frac{5}{3} \][/tex]
### Step 2: Cube the simplified base
Next, we cube the result:
[tex]\[ \left(\frac{5}{3}\right)^3 \][/tex]
Cubing a fraction involves cubing both the numerator and the denominator:
[tex]\[ \left(\frac{5}{3}\right)^3 = \frac{5^3}{3^3} = \frac{125}{27} \][/tex]
### Step 3: Evaluate the fraction
The fraction can be converted to a decimal to simplify interpretation. Performing the division:
[tex]\[ \frac{125}{27} \approx 4.629629629629631 \][/tex]
### Conclusion
Hence, the simplified value of the given expression:
[tex]\[ \left(2 - \frac{1}{3}\right)^3 \][/tex]
is approximately [tex]\( \frac{125}{27} \)[/tex] or [tex]\( 4.629629629629631 \)[/tex].
