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$$50 \times 50 \times 50 \times \cdots$$ (where there are a hundred 50s) is how many times $$100 \times 100 \times 100 \times \cdots$$ (where there are fifty 100s)?
The ratio is $$\frac{50^{100}}{100^{50}} = \frac{50^{100}}{10^{100}} = 5^{100} = 25^{50}$$. That is the product of fifty 25s.
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