what is( 6^30+6^-30)(6^30-6^-30)=3^A*8^B-3^-A*8^-B find A+B
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(6^30 + 6^ -30) (6^30 - 6^-30)
=(6^30)^2 - (6^-30)^2 since (x+y)(x-y) = x²-y²
= [6^60 ] - [6^-60] since (x^m)^n = x^mn
= [(3*2)]^60 - [(3*2)]^-60
= (3^60) *2^60 - (3^-60) (2^-60)
= (3^60) * [2³]^20 - (3^-60) [2^³]^20
= (3^60) *[8]^20 - (3^-60) [8]^-20
compare with
=3^A *8^B - 3^-A * 8 ^-B
A =60 and B =20
therefore
A+B =60+20 =80
=(6^30)^2 - (6^-30)^2 since (x+y)(x-y) = x²-y²
= [6^60 ] - [6^-60] since (x^m)^n = x^mn
= [(3*2)]^60 - [(3*2)]^-60
= (3^60) *2^60 - (3^-60) (2^-60)
= (3^60) * [2³]^20 - (3^-60) [2^³]^20
= (3^60) *[8]^20 - (3^-60) [8]^-20
compare with
=3^A *8^B - 3^-A * 8 ^-B
A =60 and B =20
therefore
A+B =60+20 =80
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