Сравните числа:
1)3^3^3 и 3^33
2)2^22 и 2^2^2
Вычислите:
1)10^4 * 10^4/25^4
2)(3/7)^3 * (7/9)^3
3)0.25^10 * 4^10
4)81 * 27^4/3^9
Ответы
Ответ дал:
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1) ![3^{3^3}=3^{27} textless 3^{33} 3^{3^3}=3^{27} textless 3^{33}](https://tex.z-dn.net/?f=3%5E%7B3%5E3%7D%3D3%5E%7B27%7D+textless++3%5E%7B33%7D)
2)![2^{22} textless 2^{2^2}=2^4 2^{22} textless 2^{2^2}=2^4](https://tex.z-dn.net/?f=2%5E%7B22%7D+textless++2%5E%7B2%5E2%7D%3D2%5E4)
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1)![10^4 * frac{10^4}{25^4}= 10^4 * (frac{10}{25})^4= (10* frac{10}{25} )^4= (frac{100}{25}) ^4=( frac{25*4}{25*1} )^4= (frac{4}{1} )^4= 10^4 * frac{10^4}{25^4}= 10^4 * (frac{10}{25})^4= (10* frac{10}{25} )^4= (frac{100}{25}) ^4=( frac{25*4}{25*1} )^4= (frac{4}{1} )^4=](https://tex.z-dn.net/?f=10%5E4+%2A++frac%7B10%5E4%7D%7B25%5E4%7D%3D+10%5E4+%2A++%28frac%7B10%7D%7B25%7D%29%5E4%3D+%2810%2A+frac%7B10%7D%7B25%7D+%29%5E4%3D+%28frac%7B100%7D%7B25%7D%29+%5E4%3D%28+frac%7B25%2A4%7D%7B25%2A1%7D+%29%5E4%3D+%28frac%7B4%7D%7B1%7D+%29%5E4%3D)
![=4^4=4^{2*2}=(4^2)^2=(16)^2=16^2=256 =4^4=4^{2*2}=(4^2)^2=(16)^2=16^2=256](https://tex.z-dn.net/?f=%3D4%5E4%3D4%5E%7B2%2A2%7D%3D%284%5E2%29%5E2%3D%2816%29%5E2%3D16%5E2%3D256)
2)![( frac{3}{7} )^3* (frac{7}{9} )^3=( frac{3}{7}* frac{7}{9} )^3= (frac{3*7*1}{3*7*3})^3 = (frac{1}{3}) ^3= frac{1^3}{3^3}= frac{1}{27} ( frac{3}{7} )^3* (frac{7}{9} )^3=( frac{3}{7}* frac{7}{9} )^3= (frac{3*7*1}{3*7*3})^3 = (frac{1}{3}) ^3= frac{1^3}{3^3}= frac{1}{27}](https://tex.z-dn.net/?f=%28+frac%7B3%7D%7B7%7D+%29%5E3%2A+%28frac%7B7%7D%7B9%7D+%29%5E3%3D%28+frac%7B3%7D%7B7%7D%2A+frac%7B7%7D%7B9%7D++%29%5E3%3D+%28frac%7B3%2A7%2A1%7D%7B3%2A7%2A3%7D%29%5E3+%3D+%28frac%7B1%7D%7B3%7D%29+%5E3%3D+frac%7B1%5E3%7D%7B3%5E3%7D%3D+frac%7B1%7D%7B27%7D++)
3)![0.25^{10} * 4^{10}=(0.25*4)^{10}=(1)^{10}=1 0.25^{10} * 4^{10}=(0.25*4)^{10}=(1)^{10}=1](https://tex.z-dn.net/?f=0.25%5E%7B10%7D+%2A+4%5E%7B10%7D%3D%280.25%2A4%29%5E%7B10%7D%3D%281%29%5E%7B10%7D%3D1)
4)![81 * frac{27^4}{3^9}= frac{81*27^4}{3^9}= frac{9^2*(3^3)^4}{3^9}=
frac{(3^2)^2*3^{3*4}}{3^9}= frac{3^{2*2}*3^{12}}{3^9}= frac{3^4*3^{12}}{3^9}= frac{3^{4+12}}{3^9} = 81 * frac{27^4}{3^9}= frac{81*27^4}{3^9}= frac{9^2*(3^3)^4}{3^9}=
frac{(3^2)^2*3^{3*4}}{3^9}= frac{3^{2*2}*3^{12}}{3^9}= frac{3^4*3^{12}}{3^9}= frac{3^{4+12}}{3^9} =](https://tex.z-dn.net/?f=81+%2A+frac%7B27%5E4%7D%7B3%5E9%7D%3D+frac%7B81%2A27%5E4%7D%7B3%5E9%7D%3D+frac%7B9%5E2%2A%283%5E3%29%5E4%7D%7B3%5E9%7D%3D%0A+frac%7B%283%5E2%29%5E2%2A3%5E%7B3%2A4%7D%7D%7B3%5E9%7D%3D+frac%7B3%5E%7B2%2A2%7D%2A3%5E%7B12%7D%7D%7B3%5E9%7D%3D+frac%7B3%5E4%2A3%5E%7B12%7D%7D%7B3%5E9%7D%3D+frac%7B3%5E%7B4%2B12%7D%7D%7B3%5E9%7D+%3D+++++)
![= frac{3^{4+12}}{3^9} =frac{3^{16}}{3^9} = frac{3^{9+7}}{3^9}= frac{3^9*3^7}{3^9*1} =frac{3^7}{1} =3^7=(3^3)^2*3^1=(27)^2*3= = frac{3^{4+12}}{3^9} =frac{3^{16}}{3^9} = frac{3^{9+7}}{3^9}= frac{3^9*3^7}{3^9*1} =frac{3^7}{1} =3^7=(3^3)^2*3^1=(27)^2*3=](https://tex.z-dn.net/?f=%3D+frac%7B3%5E%7B4%2B12%7D%7D%7B3%5E9%7D+%3Dfrac%7B3%5E%7B16%7D%7D%7B3%5E9%7D+%3D+frac%7B3%5E%7B9%2B7%7D%7D%7B3%5E9%7D%3D+frac%7B3%5E9%2A3%5E7%7D%7B3%5E9%2A1%7D++%3Dfrac%7B3%5E7%7D%7B1%7D++%3D3%5E7%3D%283%5E3%29%5E2%2A3%5E1%3D%2827%29%5E2%2A3%3D)
![=729*3=2187 =729*3=2187](https://tex.z-dn.net/?f=%3D729%2A3%3D2187)
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