Zad 1 . Zapisz w postaci jednej potęgi
Zad 2. Usun niewymierności
Zadania znajdują się na zdjęciu ;)Z góry bardzo dziękuje za rozwiązanie i zapewne się odwdzięcze ;)
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Zadanie 1.
1)![\frac{27^{-2}*\frac{1}{9}}{(\frac{1}{\sqrt3})^{4}}=[3^{-6}*3^{-2}]:[\frac{1}{3^{2}}]=3^{-8}*3^2=3^{-6} \frac{27^{-2}*\frac{1}{9}}{(\frac{1}{\sqrt3})^{4}}=[3^{-6}*3^{-2}]:[\frac{1}{3^{2}}]=3^{-8}*3^2=3^{-6}](https://tex.z-dn.net/?f=%5Cfrac%7B27%5E%7B-2%7D%2A%5Cfrac%7B1%7D%7B9%7D%7D%7B%28%5Cfrac%7B1%7D%7B%5Csqrt3%7D%29%5E%7B4%7D%7D%3D%5B3%5E%7B-6%7D%2A3%5E%7B-2%7D%5D%3A%5B%5Cfrac%7B1%7D%7B3%5E%7B2%7D%7D%5D%3D3%5E%7B-8%7D%2A3%5E2%3D3%5E%7B-6%7D)
2)![\frac{2*(0,5)^3}{(\frac{1}{2})^{-1}}=[2*0,125]:2=[2*0,125]*\frac{1}{2}=0,125=0,5^3 \frac{2*(0,5)^3}{(\frac{1}{2})^{-1}}=[2*0,125]:2=[2*0,125]*\frac{1}{2}=0,125=0,5^3](https://tex.z-dn.net/?f=%5Cfrac%7B2%2A%280%2C5%29%5E3%7D%7B%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B-1%7D%7D%3D%5B2%2A0%2C125%5D%3A2%3D%5B2%2A0%2C125%5D%2A%5Cfrac%7B1%7D%7B2%7D%3D0%2C125%3D0%2C5%5E3)
3)![125*(-5)^{-3}*0,2^2=5^3*5^{-3}*(-1)*0,2^2=-(0,2)^2 125*(-5)^{-3}*0,2^2=5^3*5^{-3}*(-1)*0,2^2=-(0,2)^2](https://tex.z-dn.net/?f=125%2A%28-5%29%5E%7B-3%7D%2A0%2C2%5E2%3D5%5E3%2A5%5E%7B-3%7D%2A%28-1%29%2A0%2C2%5E2%3D-%280%2C2%29%5E2)
4)![(\frac{10^{-3}*10}{1000})^{-2}=(\frac{10^{-2}}{10^3})^{-2}=(10^{-5})^{-2}=10^{10} (\frac{10^{-3}*10}{1000})^{-2}=(\frac{10^{-2}}{10^3})^{-2}=(10^{-5})^{-2}=10^{10}](https://tex.z-dn.net/?f=%28%5Cfrac%7B10%5E%7B-3%7D%2A10%7D%7B1000%7D%29%5E%7B-2%7D%3D%28%5Cfrac%7B10%5E%7B-2%7D%7D%7B10%5E3%7D%29%5E%7B-2%7D%3D%2810%5E%7B-5%7D%29%5E%7B-2%7D%3D10%5E%7B10%7D)
Zadanie 2.
1)![\frac{3^{\frac{1}{2}}*27^{\frac{1}{3}}}{3^{-1}*\sqrt{3}}=[\sqrt{3}*3]:[3^{-1}*3^1]=3\sqrt{3}:1=3\sqrt{3} \frac{3^{\frac{1}{2}}*27^{\frac{1}{3}}}{3^{-1}*\sqrt{3}}=[\sqrt{3}*3]:[3^{-1}*3^1]=3\sqrt{3}:1=3\sqrt{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2A27%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B3%5E%7B-1%7D%2A%5Csqrt%7B3%7D%7D%3D%5B%5Csqrt%7B3%7D%2A3%5D%3A%5B3%5E%7B-1%7D%2A3%5E1%5D%3D3%5Csqrt%7B3%7D%3A1%3D3%5Csqrt%7B3%7D)
2)![64^{\frac{1}{3}}=\sqrt[3]{64}=4 64^{\frac{1}{3}}=\sqrt[3]{64}=4](https://tex.z-dn.net/?f=64%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B64%7D%3D4)
3)![\frac{5\sqrt{2}}{3\sqrt{5}}=\frac{5\sqrt{2}*\sqrt{5}}{3*5}=\frac{\sqrt{10}}{3} \frac{5\sqrt{2}}{3\sqrt{5}}=\frac{5\sqrt{2}*\sqrt{5}}{3*5}=\frac{\sqrt{10}}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7B3%5Csqrt%7B5%7D%7D%3D%5Cfrac%7B5%5Csqrt%7B2%7D%2A%5Csqrt%7B5%7D%7D%7B3%2A5%7D%3D%5Cfrac%7B%5Csqrt%7B10%7D%7D%7B3%7D)
4)![\frac{0,25*\sqrt[3]{8}*2^{\frac{1}{2}}}{\sqrt{2}*2^{-1}}=[0,25*2*\sqrt{2}*\sqrt{2}]:[2^1*2^{-1}]=1:1=1 \frac{0,25*\sqrt[3]{8}*2^{\frac{1}{2}}}{\sqrt{2}*2^{-1}}=[0,25*2*\sqrt{2}*\sqrt{2}]:[2^1*2^{-1}]=1:1=1](https://tex.z-dn.net/?f=%5Cfrac%7B0%2C25%2A%5Csqrt%5B3%5D%7B8%7D%2A2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B%5Csqrt%7B2%7D%2A2%5E%7B-1%7D%7D%3D%5B0%2C25%2A2%2A%5Csqrt%7B2%7D%2A%5Csqrt%7B2%7D%5D%3A%5B2%5E1%2A2%5E%7B-1%7D%5D%3D1%3A1%3D1)
Ok, poprawione. Pozdrawiam :)