To rewrite the expression for \( 125 \frac{2}{3} \) as a product of identical factors, we first convert the mixed number into an improper fraction.
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Convert \( 125 \frac{2}{3} \) to an improper fraction: \[ 125 \frac{2}{3} = 125 + \frac{2}{3} = \frac{125 \cdot 3}{3} + \frac{2}{3} = \frac{375}{3} + \frac{2}{3} = \frac{375 + 2}{3} = \frac{377}{3} \]
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Now, we want to express \( \frac{377}{3} \) in a way that we can see the product of identical factors. We can multiply both the numerator and the denominator by the same number to express this in terms of factors.
To find the product of identical factors for \( 125 \frac{2}{3} \), we might want to find an appropriate factorization. A common approach is to express \( 125 \) as a whole number and then multiply.
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Since \( 125 = 5^3 \), we can express \( 125 \frac{2}{3} \) as: \[ 125 \frac{2}{3} = 5^3 \cdot \frac{2}{3} \] Thus, we can write: \[ 125 \frac{2}{3} = \frac{2 \cdot 5^3}{3} \]
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Therefore, in a simplified form where we want to emphasize the identical factors: \[ = \frac{2}{3} \cdot 5^3 \]
This way, we express the factorization clearly, with \( 5^3 \) as the product of identical factors and \( \frac{2}{3} \) as a separate fractional part.
- Finally, if we need the numerical value in simplified form: \[ 125 \frac{2}{3} = \frac{377}{3} \approx 125.67 , \text{(if approximation is allowed)} \]
Thus, the expression has been rewritten to show the product of identical factors and simplified form is \( \frac{377}{3} \) or approximately \( 125.67 \) when expressed numerically.