It means that 10 is multiplied by itself, and that it appears twice as a factor. In other words, it's the same as 10 x 10. For comparison, 10 to the third power means 10 x 10 x 10 (10 appears 3 times as a factor).
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No, it is not the same. Ten cubed is ten to the third power or 10x10x10 or 1000. Ten to the second power is 10x10 or 100.
That means that powers are used in which the base is 10. It is also implied that the exponent is an integer.
Five times ten to the third power is 5000 and three times ten to the second power is 300; 5000 + 300 = 5300.
102
200