Answer:
The statement is true
Step-by-step explanation:
The question is as following :
[tex]12^{13}-12^{12}+12^{11}[/tex] is divisible by 7 and 19, true or false?
The given expression is [tex]12^{13}-12^{12}+12^{11}[/tex]
Take [tex]12^{11}[/tex] as a common
[tex]12^{13}-12^{12}+12^{11} = 12^{11}*(12^2-12^1+12^0)\\= 12^{11} *(144-12+1)\\=12^{11} * 133\\= 12^{11} * 7 * 19[/tex]
So, [tex]12^{11} * 7 * 19[/tex] divided 7 = [tex]12^{11} * 19[/tex]
And [tex]12^{11} * 7 * 19[/tex] divided 19 = [tex]12^{11} * 7[/tex]
[tex]12^{13}-12^{12}+12^{11}[/tex] is divisible by 7 and 19 (True)
