To rewrite \( 125 \frac{2}{3} \) as a product of identical factors, we first convert the mixed number into an improper fraction.
- Convert \( 125 \frac{2}{3} \) to an improper fraction:
\[ 125 \frac{2}{3} = \frac{(125 \times 3) + 2}{3} = \frac{375 + 2}{3} = \frac{377}{3} \]
- Next, we will rewrite \( \frac{377}{3} \) in a form that allows us to express it as a product of identical factors. First, compute \( 377 \).
Looking for perfect squares, we approximate \( 377 \):
\[ 377 = 25 \times 15.08 \text{ (not a perfect square)} \]
Since \( 377 \) is not a perfect square, we can try to approximate or find its prime factors. Upon checking divisibility, we find:
- \( 377 \) is not divisible by \( 2, 3, \) or \( 5 \).
However, observing \( 377 \):
\[ 377 = 13 \times 29 \]
Therefore, \( 125 \frac{2}{3} \) can be represented, in its entirety, in simplified form as:
- Numerator: \( 377 = 13 \times 29 \)
- Denominator: \( 3 \)
Thus, we bring it back to the mixed number form, yielding a fractional representation:
Finally, as \( 125 \frac{2}{3} = \frac{377}{3} \), this cannot be expressed directly as a product of identical factors.
Reiterating, it does not translate neatly into anything requiring identical multiplication factors in the form of squares or cubes. Therefore:
The final simplified form is:
\[ \frac{377}{3} \]
If needing any alternative expression, consider:
\(\sqrt{125 \frac{2}{3} \cdot 3}\) or approximate another style representation as an expression but not a product of identical factors.