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Without actually multiplying, you would have to estimate the zeroes as

2.122 = 12,269,432.738610566

10022 = 1044 [ (102)22 ]

So there would be between 22 and 35 zeroes including the significant figures.

* 21022 is about 1.2269432738610566 x 1051

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10y ago
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Q: How many zeros are in the figure 210 to the power of 22?
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