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