7^6 + 7^5 - 7^4 = 7^4*7^2 + 7^4*7^1 - 7^4*1
7^6 + 7^5 - 7^4 = 7^4(7^2 + 7^1 - 1)
7^6 + 7^5 - 7^4 = 7^4(49 + 7 - 1)
7^6 + 7^5 - 7^4 = 7^4*55
7^6 + 7^5 - 7^4 = 7^4*5*11
7^6 + 7^5 - 7^4 = 11*5*7^4
7^6 + 7^5 - 7^4 = 11*k
Since the number is in the form 11*k, where k = 5*7^4, this proves that 7^6 + 7^5 - 7^4 is a multiple of 11.
The Expression came in two parts, we started by solving the first part and getting a whole number and the second part was used to divide the first part.
The answer is 12005
Given Data
we have the expression
7^6+7^5−7^4 by 11
The dividend = 7^6+7^5−7^4
The divisor = 11
Let us express the dividend as a whole number
7^6+7^5−7^4 = 117649 + 16807 - 2401
7^6+7^5−7^4 = 132055
Hence the expression 7^6+7^5−7^4 by 11
= 132055/11
= 12005 ans
Learn more about division of numbers here:
https://brainly.com/question/25289437
