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poprawna odpowiedź to
5∛x + ∛x²
Doprowadź do najprostszej postaci.
Proszę o przedstawienie również toku myślenia.
poprawna odpowiedź to
5∛x + ∛x²
irenas
![[\frac{125^{\frac{2}{3}}-(0,2)^{-1}}{(0,5)^{-2}}\cdot(0,2)^{-3}]^{\frac{3}{4}}=[\frac{(5^3)^{\frac{2}{3}}-(\frac{1}{5})^{-1}}{(\frac{1}{2}^{-2}}\cdot(\frac{1}{5})^{-3}]^{\frac{3}{4}}=\\=[\frac{5^2-5}{4}\cdot5^3]^{\frac{3}{4}}=[\frac{25-5}{4}\cdot5^3]^{\frac{3}{4}}=\\=[\frac{20}{4}\cdot5^3]^{\frac{3}{4}}=[5\cdot5^3]^{\frac{3}{4}}=((5^4)^{\frac{3}{4}}=5^3=125](https://tex.z-dn.net/?f=%5B%5Cfrac%7B125%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D-%280%2C2%29%5E%7B-1%7D%7D%7B%280%2C5%29%5E%7B-2%7D%7D%5Ccdot%280%2C2%29%5E%7B-3%7D%5D%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5B%5Cfrac%7B%285%5E3%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D-%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7B-1%7D%7D%7B%28%5Cfrac%7B1%7D%7B2%7D%5E%7B-2%7D%7D%5Ccdot%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7B-3%7D%5D%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5C%5C%3D%5B%5Cfrac%7B5%5E2-5%7D%7B4%7D%5Ccdot5%5E3%5D%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5B%5Cfrac%7B25-5%7D%7B4%7D%5Ccdot5%5E3%5D%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5C%5C%3D%5B%5Cfrac%7B20%7D%7B4%7D%5Ccdot5%5E3%5D%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5B5%5Ccdot5%5E3%5D%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%28%285%5E4%29%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D5%5E3%3D125 "[\frac{125^{\frac{2}{3}}-(0,2)^{-1}}{(0,5)^{-2}}\cdot(0,2)^{-3}]^{\frac{3}{4}}=[\frac{(5^3)^{\frac{2}{3}}-(\frac{1}{5})^{-1}}{(\frac{1}{2}^{-2}}\cdot(\frac{1}{5})^{-3}]^{\frac{3}{4}}=\\=[\frac{5^2-5}{4}\cdot5^3]^{\frac{3}{4}}=[\frac{25-5}{4}\cdot5^3]^{\frac{3}{4}}=\\=[\frac{20}{4}\cdot5^3]^{\frac{3}{4}}=[5\cdot5^3]^{\frac{3}{4}}=((5^4)^{\frac{3}{4}}=5^3=125")
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krysta
![\left [ \frac{125^{\frac{2}{3}}-(0,2)^{-1}}{(0,5)^{-2}}*(0,2)^{-3} \right ] ^{\frac{3}{4}} = \left [ \frac{ (5^3)^{\frac{2}{3}}-( \frac{2}{10})^{-1}}{(\frac{ 5}{10})^{-2}}*( \frac{2}{10})^{-3} \right ] ^{\frac{3}{4}} = \\\\= \left [\frac{ 5 ^{3*\frac{2}{3}}-( \frac{1}{5})^{-1}}{(\frac{ 1}{2})^{-2}}*( \frac{1}{5})^{-3} \right ] ^{\frac{3}{4}} = \left [ \frac{ 5 ^{2}-( \frac{5}{1})^{ 1}}{(\frac{2}{ 1})^{ 2}}*( \frac{5}{1})^{ 3} \right ] ^{\frac{3}{4}} =\left [ \frac{ 25-5}{4}*125 \right ] ^{\frac{3}{4}}=](https://tex.z-dn.net/?f=%5Cleft+%5B+%5Cfrac%7B125%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D-%280%2C2%29%5E%7B-1%7D%7D%7B%280%2C5%29%5E%7B-2%7D%7D%2A%280%2C2%29%5E%7B-3%7D+%5Cright+%5D+%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D+%3D+%5Cleft+%5B+%5Cfrac%7B+%285%5E3%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D-%28+%5Cfrac%7B2%7D%7B10%7D%29%5E%7B-1%7D%7D%7B%28%5Cfrac%7B+5%7D%7B10%7D%29%5E%7B-2%7D%7D%2A%28+%5Cfrac%7B2%7D%7B10%7D%29%5E%7B-3%7D+%5Cright+%5D+%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D+%3D+%5C%5C%5C%5C%3D+%5Cleft+%5B%5Cfrac%7B+5+%5E%7B3%2A%5Cfrac%7B2%7D%7B3%7D%7D-%28+%5Cfrac%7B1%7D%7B5%7D%29%5E%7B-1%7D%7D%7B%28%5Cfrac%7B+1%7D%7B2%7D%29%5E%7B-2%7D%7D%2A%28+%5Cfrac%7B1%7D%7B5%7D%29%5E%7B-3%7D+%5Cright+%5D+%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D+%3D+%5Cleft+%5B+%5Cfrac%7B+5+%5E%7B2%7D-%28+%5Cfrac%7B5%7D%7B1%7D%29%5E%7B+1%7D%7D%7B%28%5Cfrac%7B2%7D%7B+1%7D%29%5E%7B+2%7D%7D%2A%28+%5Cfrac%7B5%7D%7B1%7D%29%5E%7B+3%7D+%5Cright+%5D+%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D+%3D%5Cleft+%5B+%5Cfrac%7B+25-5%7D%7B4%7D%2A125+%5Cright+%5D+%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D "\left [ \frac{125^{\frac{2}{3}}-(0,2)^{-1}}{(0,5)^{-2}}*(0,2)^{-3} \right ] ^{\frac{3}{4}} = \left [ \frac{ (5^3)^{\frac{2}{3}}-( \frac{2}{10})^{-1}}{(\frac{ 5}{10})^{-2}}*( \frac{2}{10})^{-3} \right ] ^{\frac{3}{4}} = \\\\= \left [\frac{ 5 ^{3*\frac{2}{3}}-( \frac{1}{5})^{-1}}{(\frac{ 1}{2})^{-2}}*( \frac{1}{5})^{-3} \right ] ^{\frac{3}{4}} = \left [ \frac{ 5 ^{2}-( \frac{5}{1})^{ 1}}{(\frac{2}{ 1})^{ 2}}*( \frac{5}{1})^{ 3} \right ] ^{\frac{3}{4}} =\left [ \frac{ 25-5}{4}*125 \right ] ^{\frac{3}{4}}=")
![=\left [ \frac{ 20}{4}*5^3 \right ] ^{\frac{3}{4}} =\left [ 5*5^3 \right ] ^{\frac{3}{4}}= ( 5^{1+3} ) ^{\frac{3}{4}}=(5^{4})^{\frac{3}{4}}= 5 ^{4*\frac{3}{4}} =5^3=125](https://tex.z-dn.net/?f=%3D%5Cleft+%5B+%5Cfrac%7B+20%7D%7B4%7D%2A5%5E3+%5Cright+%5D+%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D+%3D%5Cleft+%5B+5%2A5%5E3+%5Cright+%5D+%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D+%28+5%5E%7B1%2B3%7D+%29+%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%285%5E%7B4%7D%29%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D+5+%5E%7B4%2A%5Cfrac%7B3%7D%7B4%7D%7D+%3D5%5E3%3D125 "=\left [ \frac{ 20}{4}*5^3 \right ] ^{\frac{3}{4}} =\left [ 5*5^3 \right ] ^{\frac{3}{4}}= ( 5^{1+3} ) ^{\frac{3}{4}}=(5^{4})^{\frac{3}{4}}= 5 ^{4*\frac{3}{4}} =5^3=125")
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