Expressed in figures, 1015 = 1,000,000,000,000,000. This would be called one quadrillion in US and modernday UK English and one thousand billion in Commonwealth English.
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10^15 = 1,000,000,000,000,000 (one quadrillion).
"Second power" means that you multiply something with itself. In this case, (10 + 15) (10 + 15).
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10 to the power of 15 when multiplying items with the same base (in this case 10) you simply add the powers
10 to the power of 15