Zjednodušte výraz

Anonym Jynocak08.09.2018 20:16 Nahlásit
Jak

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Cenobita.08.09.2018 22:47 (Upr. 08.09.2018 23:54) Nahlásit
√(2³√4) / ³√(2√√8) =
(8*4)^(1/6) / (√(16*8))^(1/6) =
(8*4 / √(16*8) )^(1/6) =
(8*4 / √(16*8) * √(16*8)/√(16*8) )^(1/6) =
(8*4 / (16*8) * √(16*8) )^(1/6) =
(1 / 4 * √(16*8) )^(1/6) =
( √(16*8/16) )^(1/6) =
( √8 )^(1/6) =
( √(2*4) )^(1/6) =

= (8) ^(1/12)
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=(2)^(1/4)
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nebo jinak:

√(2³√4) / ³√(2√√8) =
√(³√(8*4)) / ³√(√√(16*8)) =
(8*4)^(1/6) / (16*8)^(1/12) =
(8*4*8*4)^(1/12) / (16*8)^(1/12) =
( (8*4*8*4)/(16*8) )^(1/12) =
( 8 )^(1/12) =
( 2*2*2 )^(1/(3*4)) =

= ( 2 )^(1/4)
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