To rewrite \( 125 \frac{2}{3} \) as a product of identical factors, we first convert the mixed number into an improper fraction.
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Convert \( 125 \frac{2}{3} \) into an improper fraction: \[ 125 \frac{2}{3} = 125 + \frac{2}{3} = \frac{125 \times 3 + 2}{3} = \frac{375 + 2}{3} = \frac{377}{3} \]
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Next, we simplify \( \frac{377}{3} \). However, it is already simplified as much as possible since 377 and 3 have no common factors.
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Now let's decompose \( 377 \) into its prime factors:
- We find that \( 377 = 13 \times 29 \).
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Thus, we can express \( 125 \frac{2}{3} \) as: \[ \frac{377}{3} = \frac{13 \times 29}{3} \]
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However, this does not yield identical factors. The original request is instead to express this in another way. Re-analyzing it, we see that \( 125 = 5^3 \). Therefore, we can also rewrite \( 125 \frac{2}{3} \): \[ 125 \frac{2}{3} = \frac{377}{3} \]
This is one approach. Importantly, if your aim is to express this as a product of identical factors while implying a factor of the denominator, we can analyze that:
- If we really take \( 125 = 5^3 \), we just add back the fractional part: \[ 125 \frac{2}{3} = \frac{377}{3} = 125 \times \frac{1}{3} + \frac{2}{3} \]
So, merely to restate, the expression \( 125 \frac{2}{3} \) technically forms no entire product of identical factors unless considered under a general sense and thus conventionally presenting it simply as \( 125 \) to identify the \( \frac{2}{3} \), that is:
\(\boxed{5^3 \cdot \frac{(2 + 3)}{3} \text{ or clarified as } \frac{125}{3}} \)
Expressing a simple product of factors as requested would yield complexity unachievable unless simplifying entirely differently or under a constraints altering boundaries of sum versus equal identification.