Ashishmathew01081987 wrote:
\(3^{13} + 9^5 = 3^{13} + 3^{10} = 3^{23}\)
\(3^{13} - 9^5 = 3^{13} - 3^{10} = 3^3\)
hi this is incorrect
\(a^{b} . a^{c} = a^{b+c}\)
\(also,\) \(a^{b}. a^{-c} = a^{b-c}\)
PareshGmat wrote:
The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is
A: \(3^{13}\)
B: \(3^{12} - 9^5\)
C: \(2*3^{12}\)
D: \(3^{11} - 9^5\)
E: \(3^{11}\)
\((3^{13} + 9^5)\) = \(3^{13} + 3^{10}\)
\(=3^{10} (3^{3} +1 )
=3^{10}28
= 2^{2}. 7 . 3^{10}\) -------------------------1)
\((3^{13} - 9^5)\) = \(3^{13} - 3^{10}\)
\(= 3^{10} (3^{3} - 1 )
=3^{10}26
=2 . 13 . 3^{10}\) -----------------------------2)
as can be seen the highest common factor of 1 and 2 is \(2 . 3^{10}\)
option D = \(3^{11} - 9^5\)
\(= 3^{11} - 3^{10}
=3^{10} (3-1)
= 2 . 3^{10}\)
hence answer is D