Question

Rewrite 125 2/3 as a product of identical factors to simplify

Answer 1

To rewrite \( 125 \frac{2}{3} \) as a product of identical factors, we first convert the mixed number into an improper fraction.

1. Convert \( 125 \frac{2}{3} \) to an improper fraction:
\[
125 \frac{2}{3} = 125 + \frac{2}{3} = \frac{375}{3} + \frac{2}{3} = \frac{375 + 2}{3} = \frac{377}{3}
\]

Next, we want to simplify \( \frac{377}{3} \) and find identical factors. We can express the number \( 377 \) as the product of its prime factors.

2. Factor \( 377 \):
\[
377 = 13 \times 29
\]

3. Therefore, we cannot simplify \( \frac{377}{3} \) further into identical factors in a simple way like \( a^n \) format.

However, there's insight to be provided here: If you want to keep it as an improper fraction and factor out the number \( 377 \) and the denominator separately, we can express it as:
\[
\frac{377}{3} = \frac{13 \times 29}{3}
\]

Thus, while we cannot simplify it neatly as identical factors, it maintains its form, and if any further manipulation or context is given (for instance, finding a decimal representation or further operations), we could move from here.

In summary, \( 125 \frac{2}{3} \) simplifies into a fraction \( \frac{377}{3} \), and it can be observed in terms of its prime factors \( 13 \) and \( 29 \).