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When (10^5 * 10^77 / (10^15 ) / (10^15)^4 is written as a single integer with no exponents, it is a 1 followed by one or more zeroes. How many zeroes are there?

 Apr 9, 2023
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(10^5 * 10^77) / (10^15 ) / (10^15)^4

 

To start, we can set 10^5 * 10^77 to 10^82, as multiplying exponets is the same as adding them.

 

next, we can set (10^15)^4 to 10^60, as its the same thing as multiplying 10^15 to itself four times, which as we have stated is the same thing as adding. (15+15+15+15=60)

 

finally, dividing with exponents is the same as subtracting them, so we take 10^82, and subtract 10^15, and 10^60, (82-15-60), so our final exponent is 10^7.

 

10^7 is the same thing as 10,000,000, or 10 with 7 zeros behind it.

 

Our final answer is 7.

 Apr 9, 2023

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