Oblicz:
a) (729/ 64) do potęgi - 2/3
b) 5 do pot. -4/3 : 25 do pot. -3/2
c) (12 i 1/4) do pot. 1/2 * 4
d) (81 do pot. 0,5 * 9 do pot. -1) do pot. -1/2
e) (0, 25) do pot. -1/2
f) (-32) do pot. 4/5
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Oblicz:
a) (729/ 64) do potęgi - 2/3=64/729^2/3=pierw3 st z (64/729)^2=
=(4/9)^2=16/81
b) 5 do pot. -4/3 : 25 do pot. -3/2=1/5^4/5: 1/25^3/2=
=1/5^4/5: (1/5^2)^3/2=1/5^4/5 : 1/5 ^3=1/5^(4/5-3)=1/5^(-11/5)=
=5^11/5=pierw 5 st z 11^2=
c) (12 i 1/4) do pot. 1/2 * 4=49/4^1/2 * 4 =7/2 * 4= 14
d) (81 do pot. 0,5 * 9 do pot. -1) do pot. -1/2=
=(pierw z 81 * 1/9)^-1/2=
=( 9*1/9)^-1/2=1
e) (0, 25) do pot. -1/2=1/4^-1/2=pierw z 4=2
f) (-32) do pot. 4/5=pierw 5 st. z -32^4=2^4=16
a)![a) {\frac{729}{64}}^{-\frac{2}{3}}=\frac{729^{-\frac{2}{3}}}{64^{-\frac{2}{3}}}}\\ 729^{-\frac{2}{3}}=729^{-2*\frac{1}{3}}=(\sqrt[3]{729})^{-2}=(\sqrt[3]{9*9*9})^{-2}=9^{-2}=9^{-1*2}=81^{-1} a) {\frac{729}{64}}^{-\frac{2}{3}}=\frac{729^{-\frac{2}{3}}}{64^{-\frac{2}{3}}}}\\ 729^{-\frac{2}{3}}=729^{-2*\frac{1}{3}}=(\sqrt[3]{729})^{-2}=(\sqrt[3]{9*9*9})^{-2}=9^{-2}=9^{-1*2}=81^{-1}](https://tex.z-dn.net/?f=a%29+%7B%5Cfrac%7B729%7D%7B64%7D%7D%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Cfrac%7B729%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%7D%7B64%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%7D%7D%5C%5C+729%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%3D729%5E%7B-2%2A%5Cfrac%7B1%7D%7B3%7D%7D%3D%28%5Csqrt%5B3%5D%7B729%7D%29%5E%7B-2%7D%3D%28%5Csqrt%5B3%5D%7B9%2A9%2A9%7D%29%5E%7B-2%7D%3D9%5E%7B-2%7D%3D9%5E%7B-1%2A2%7D%3D81%5E%7B-1%7D)
![64^{-\frac{2}{3}}=4^{3*(-\frac{2}{3})}=4^{1*(-\frac{2}{1})}=4^{-2}=4^{-1*2}=16^{-1} 64^{-\frac{2}{3}}=4^{3*(-\frac{2}{3})}=4^{1*(-\frac{2}{1})}=4^{-2}=4^{-1*2}=16^{-1}](https://tex.z-dn.net/?f=64%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%3D4%5E%7B3%2A%28-%5Cfrac%7B2%7D%7B3%7D%29%7D%3D4%5E%7B1%2A%28-%5Cfrac%7B2%7D%7B1%7D%29%7D%3D4%5E%7B-2%7D%3D4%5E%7B-1%2A2%7D%3D16%5E%7B-1%7D)
![\frac{81^{-1}}{16^{-1}}=(\frac{81}{16})^{-1}=\frac{16}{81} \frac{81^{-1}}{16^{-1}}=(\frac{81}{16})^{-1}=\frac{16}{81}](https://tex.z-dn.net/?f=%5Cfrac%7B81%5E%7B-1%7D%7D%7B16%5E%7B-1%7D%7D%3D%28%5Cfrac%7B81%7D%7B16%7D%29%5E%7B-1%7D%3D%5Cfrac%7B16%7D%7B81%7D)
Pierwszy przykład dokładnie opisany żeby zrozumieć zasadę
b)
Dalej sensu liczenia nie widzę - bo nie wyjdze z tego czytelna liczba, a i b dodane dla ułatwienia(nie powinno się tak zapisywać)
c)
Cos mysle ze nie o taki przykład chodziło
d)O co chodziło dokładnie, okazja nauczyć się podstaw texa :)
e)![0,25^{-1/2}=0,25^{-1*1/2}=(\sqrt{0,25})^{-1}=(0,5)^{-1}=(\frac{1}{2})^{-1}=(\frac{2}{1})=2 0,25^{-1/2}=0,25^{-1*1/2}=(\sqrt{0,25})^{-1}=(0,5)^{-1}=(\frac{1}{2})^{-1}=(\frac{2}{1})=2](https://tex.z-dn.net/?f=0%2C25%5E%7B-1%2F2%7D%3D0%2C25%5E%7B-1%2A1%2F2%7D%3D%28%5Csqrt%7B0%2C25%7D%29%5E%7B-1%7D%3D%280%2C5%29%5E%7B-1%7D%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-1%7D%3D%28%5Cfrac%7B2%7D%7B1%7D%29%3D2)
f)![(-32)^{4/5}=((-2)*(-2)*(-2)*(-2)*(-2))^{4/5}=(-2^5)^{4/5}=\\ =(-2)^{5*\frac{4}{5}}=(-2)^{1*\frac{4}{1}}=(-2)^{4}=(-2)(-2)(-2)(-2)=4*4=16 (-32)^{4/5}=((-2)*(-2)*(-2)*(-2)*(-2))^{4/5}=(-2^5)^{4/5}=\\ =(-2)^{5*\frac{4}{5}}=(-2)^{1*\frac{4}{1}}=(-2)^{4}=(-2)(-2)(-2)(-2)=4*4=16](https://tex.z-dn.net/?f=%28-32%29%5E%7B4%2F5%7D%3D%28%28-2%29%2A%28-2%29%2A%28-2%29%2A%28-2%29%2A%28-2%29%29%5E%7B4%2F5%7D%3D%28-2%5E5%29%5E%7B4%2F5%7D%3D%5C%5C+%3D%28-2%29%5E%7B5%2A%5Cfrac%7B4%7D%7B5%7D%7D%3D%28-2%29%5E%7B1%2A%5Cfrac%7B4%7D%7B1%7D%7D%3D%28-2%29%5E%7B4%7D%3D%28-2%29%28-2%29%28-2%29%28-2%29%3D4%2A4%3D16)
Mam nadzieje że zrozumiesz jak to działa, a nie tylko to przepiszesz jako zadanie.