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Simplify and express with positive exponents:

\(\frac{16}{25} \times 625 \times \frac{25}{4} \times \frac{125}{8}\)

Answer :

Final Answer:

The simplified expression with positive exponents for 16/25 * 625 * 25/4 * 125/8 is 390625/8 or 48828.125.

Explanation:

1. Let's begin by simplifying each fraction separately:

16/25 remains as 16/25 as it cannot be simplified further.

625 is an integer, so we'll consider it as 625/1.

25/4 remains as 25/4 as it's already simplified.

125/8 remains as 125/8 since there's no further simplification needed.

2. Now, multiplying the numerators together and denominators together:

Numerator: 16 x 625 x 25 x 125 = 3125000.

Denominator: 25 x 1 x 4 x 8 = 800.

So, the fraction becomes: 3125000/800.

3. To simplify this fraction, we'll divide both the numerator and the denominator by their greatest common factor, which is 800:

3125000 ÷ 800 = 390625

800 ÷ 800 = 1

This means the fraction is equal to 390625/1, or simply 390625. However, given the original problem, the fraction remains 390625/8 or 48828.125 when expressed as a decimal.

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