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dan00001
@dan00001
July 2022
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216 в степени n-1 делить на произведение 3 * 6 в степени n * 2 в степени 2n-1 * 3 в степени 2n+1
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m11m
Verified answer
216^(n-1)
=
3*6^n * 2^(2n-1)*3^(2n+1)
=
(6³)^(n-1)
=
3*(2*3)^n * 2^(2n-1) * 3^(2n+1)
=
(2*3)^(3(n-1))
=
2^(3n-3) * 3^(3n-3)
=
3*2^n*3^n*2^(2n-1) * 3^(2n+1) 3^(1+n+2n+1) * 2^(n+2n-1)
=
2^(3n-3) * 3^(3n-3)
= 2^(3n-3-3n+1) * 3^(3n-3-3n-2) =
3^(3n+2) * 2^(3n-1)
=2⁻² * 3⁻⁵ =
1
=
1
=
1
2² * 3⁵ 4*243 972
22 votes
Thanks 41
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Answers & Comments
Verified answer
216^(n-1) =3*6^n * 2^(2n-1)*3^(2n+1)
= (6³)^(n-1) =
3*(2*3)^n * 2^(2n-1) * 3^(2n+1)
= (2*3)^(3(n-1)) = 2^(3n-3) * 3^(3n-3) =
3*2^n*3^n*2^(2n-1) * 3^(2n+1) 3^(1+n+2n+1) * 2^(n+2n-1)
= 2^(3n-3) * 3^(3n-3) = 2^(3n-3-3n+1) * 3^(3n-3-3n-2) =
3^(3n+2) * 2^(3n-1)
=2⁻² * 3⁻⁵ = 1 = 1 = 1
2² * 3⁵ 4*243 972