+4 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?
+6 (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.
