To rewrite the expression \( 125 \frac{2}{3} \) as a product of identical factors, we first convert it to an improper fraction:
\[ 125 \frac{2}{3} = 125 + \frac{2}{3} = \frac{125 \times 3}{3} + \frac{2}{3} = \frac{375}{3} + \frac{2}{3} = \frac{375 + 2}{3} = \frac{377}{3} \]
Next, we have the fraction \( \frac{377}{3} \). To express \( 125 \frac{2}{3} \) in terms of identical factors, we can start by recognizing the value of \( 125 \) in the context of perfect cubes since \( 125 = 5^3 \). However, we need to simplify this further.
To find the decimal or mixed number approximation of \( \frac{377}{3} \):
\[ \frac{377}{3} = 125 + \frac{2}{3} = 125.6667 \approx 125.67 \]
To express \( 125 \frac{2}{3} \) efficiently as a product, let’s consider converting it directly into decimal and factors format.
As the factors, \( 125 \frac{2}{3} \) implies:
\[ = \frac{377}{3} \]
This form does not easily yield discovery into similar identical factors, so we go back to \(125 \) as a factor to find perfect cubes. We can also express \( 125 \) as \( (5)^3 \):
Therefore, rewriting \( 125 \frac{2}{3} = 5^3 \times \frac{2}{3} \):
Putting it together will result in the expression:
\[ = 5^3 \times \left(\frac{2}{3}\right) \text{ or } \frac{5^3 \cdot 2}{3} \]
Since there isn’t an easy way to discover identical factors for multiplication needed beyond this expression involving the \( 125 \) as cube, thus we keep it simplified as \( \frac{5^3 \cdot 2}{3} \).
In conclusion, the best form to submit would be:
\[ \frac{5^3 \cdot 2}{3} \text{ or written as a combined fraction of unique factors} \]