Respuesta :
Factor out the GCF 7^6
7^8 - 7^7 + 7^6 = 7^6(7^2 - 7^1 + 7^0)
7^8 - 7^7 + 7^6 = 7^6(49 - 7 + 1)
7^8 - 7^7 + 7^6 = 7^6(42 + 1)
7^8 - 7^7 + 7^6 = 7^6*43
The term 43 is part of the final factorization after fully simplifying. We don't need to find the value of 7^6. This is enough to prove that the original expression is divisible by 43.
Exponent is the number which are placed over the a number as a subscript. This subscript exponent over the number refers that the number of times the base number has to be multiplied by itself. The result of the given expression is 43 times [tex]7^6[/tex]. Thus it is divisible by 43.
Given-
Let the result of the given expression is X. Thus,
[tex]x=7^8-7^7+7^6[/tex]
What is exponent?
Exponent is the number which are placed over the a number as a subscript. This subscript exponent over the number refers that the number of times the base number has to be multiplied by itself.
By the rule of the product of the exponent power when both the integer have same base value then add the exponents to get the solution. Thus we can rewrite the above equation as,
[tex]x=7^{6+2}-7^{6+1}+7^6[/tex]
[tex]x=7^6\times 7^2-7^6\times7^1+7^6[/tex]
[tex]x=7^6( 7^2-7+1)[/tex]
[tex]x=7^6(49-4+1)[/tex]
[tex]x=7^6\times43[/tex]
As the result of the given expression is 43 times [tex]7^6[/tex]. Thus it is divisible by 43.
Learn more about the exponents here;
https://brainly.com/question/5497425
