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?

Ashdog791 Apr 9, 2023

#1**+1 **

(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.**

CastleCrusher Apr 9, 2023