what is the number of zeros at the end of the product 5^5×10^10×15^15×.....×125^125
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We only have to consider the powers of multiplies of 10 in this product.
In this product, powers of multiplies of 10 like 10^10, 20^20, 30^30 upto 120^120 are multiplied.
Well,
→ 10^10 ends in 10 zeros.
→ 20^20 ends in 20 zeros.
→ 30^30 ends in 30 zeros.
Likewise, to 120^120,
→ 120^120 ends in 120 zeros.
Hence total no. of zeros will be,
10 + 20 + 30 + ...... + 120
=> 10(1 + 2 + 3 + ...... + 12)
=> (10 × 12 × 13) / 2
=> 780
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