Помогите решить пожалуйста, алгебра 7 класс , спасибо заранее
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Ответил zhenyaM2002
0
№1.
![2^{-2} * 2^{-2} = 2^{-2 +(-2) } = 2^{-4} = frac{1}{2^4} = frac{1}{16} \ \ \
frac{2^{-3} *2^{-7}}{2^{-5} * 2^{-4}} = frac{2^{-10}}{2^{-9}} =2^{-10-(-9)}=2^{-1} = frac{1}{2^1} = 0.5 \ \ \
frac{(7^{-3})^{-2} * 7^{-5}}{7^{-2} * 7^3} = frac{7^{-3*(-2)} * 7^{-5}}{7^{-2+3}} = frac{7^{6+ (-5)}}{7^1} = frac{7^1}{7^1} = 1 \ \ \
( frac{1}{5} )^{-2} * ( frac{1}{5} )^3 = (5^{-1})^{-2} * (5^{-1})^3 = 5^{-1*(-2) + (-1)*3} = \ \ = 5^{-1} = frac{1}{5} =0.2](https://tex.z-dn.net/?f=2%5E%7B-2%7D++%2A+2%5E%7B-2%7D+%3D+2%5E%7B-2+%2B%28-2%29+%7D++%3D+2%5E%7B-4%7D+%3D++frac%7B1%7D%7B2%5E4%7D++%3D++frac%7B1%7D%7B16%7D++%5C++%5C++%5C+%0A+frac%7B2%5E%7B-3%7D+%2A2%5E%7B-7%7D%7D%7B2%5E%7B-5%7D+%2A+2%5E%7B-4%7D%7D++%3D++frac%7B2%5E%7B-10%7D%7D%7B2%5E%7B-9%7D%7D+%3D2%5E%7B-10-%28-9%29%7D%3D2%5E%7B-1%7D+%3D++frac%7B1%7D%7B2%5E1%7D++%3D+0.5+%5C++%5C++%5C+%0A+frac%7B%287%5E%7B-3%7D%29%5E%7B-2%7D++%2A+7%5E%7B-5%7D%7D%7B7%5E%7B-2%7D+%2A+7%5E3%7D+%3D++frac%7B7%5E%7B-3%2A%28-2%29%7D+%2A+7%5E%7B-5%7D%7D%7B7%5E%7B-2%2B3%7D%7D+%3D++frac%7B7%5E%7B6%2B+%28-5%29%7D%7D%7B7%5E1%7D++%3D++frac%7B7%5E1%7D%7B7%5E1%7D++%3D++1+%5C++%5C++%5C+%0A%28+frac%7B1%7D%7B5%7D+%29%5E%7B-2%7D+++%2A+%28+frac%7B1%7D%7B5%7D+%29%5E3++%3D+%285%5E%7B-1%7D%29%5E%7B-2%7D++%2A+%285%5E%7B-1%7D%29%5E3++%3D+5%5E%7B-1%2A%28-2%29+%2B+%28-1%29%2A3%7D++%3D+%5C++%5C+%3D+5%5E%7B-1%7D+%3D++frac%7B1%7D%7B5%7D+%3D0.2 "2^{-2} * 2^{-2} = 2^{-2 +(-2) } = 2^{-4} = frac{1}{2^4} = frac{1}{16} \ \ \
frac{2^{-3} *2^{-7}}{2^{-5} * 2^{-4}} = frac{2^{-10}}{2^{-9}} =2^{-10-(-9)}=2^{-1} = frac{1}{2^1} = 0.5 \ \ \
frac{(7^{-3})^{-2} * 7^{-5}}{7^{-2} * 7^3} = frac{7^{-3*(-2)} * 7^{-5}}{7^{-2+3}} = frac{7^{6+ (-5)}}{7^1} = frac{7^1}{7^1} = 1 \ \ \
( frac{1}{5} )^{-2} * ( frac{1}{5} )^3 = (5^{-1})^{-2} * (5^{-1})^3 = 5^{-1*(-2) + (-1)*3} = \ \ = 5^{-1} = frac{1}{5} =0.2")
№2.
![а^{-3} = frac{1}{a^3} \ \
(5x)^{-2} = frac{1}{(5x)^2} = frac{1}{25x^2} \ \
xy^{-1} = x * frac{1}{y^1} = frac{x}{1} * frac{1}{y}= frac{x}{y} \ \
3m^2n^{-2} = 3m^2 * frac{1}{n^2} = frac{3m^2}{n^2} \ \
a^{-2} +b^{-2} = frac{1}{a^2} + frac{1}{b^2} = frac{b^2+a^2}{a^2b^2} \ \
(u-v)^{-2} = frac{1}{(u-v)^2} \ \
-10yz^{-19} =-10y * frac{1}{z^{19}} = - frac{10y}{z^{19}} \ \
2(a+c)^{-3} = frac{2}{(a+c)^3}](https://tex.z-dn.net/?f=%D0%B0%5E%7B-3%7D++%3D++frac%7B1%7D%7Ba%5E3%7D++%5C++%5C+%0A%285x%29%5E%7B-2%7D+%3D++frac%7B1%7D%7B%285x%29%5E2%7D++%3D++frac%7B1%7D%7B25x%5E2%7D++%5C++%5C+%0Axy%5E%7B-1%7D+%3D+x++%2A++frac%7B1%7D%7By%5E1%7D+%3D++frac%7Bx%7D%7B1%7D++%2A+frac%7B1%7D%7By%7D%3D+frac%7Bx%7D%7By%7D++%5C++%5C+%0A3m%5E2n%5E%7B-2%7D+%3D+3m%5E2++%2A++frac%7B1%7D%7Bn%5E2%7D+%3D+frac%7B3m%5E2%7D%7Bn%5E2%7D++%5C++%5C+%0Aa%5E%7B-2%7D++%2Bb%5E%7B-2%7D+%3D++frac%7B1%7D%7Ba%5E2%7D++%2B+frac%7B1%7D%7Bb%5E2%7D+%3D+frac%7Bb%5E2%2Ba%5E2%7D%7Ba%5E2b%5E2%7D++%5C++%5C+%0A%28u-v%29%5E%7B-2%7D+%3D++frac%7B1%7D%7B%28u-v%29%5E2%7D++%5C++%5C+%0A-10yz%5E%7B-19%7D+%3D-10y+%2A++frac%7B1%7D%7Bz%5E%7B19%7D%7D++%3D++-+frac%7B10y%7D%7Bz%5E%7B19%7D%7D++%5C++%5C+%0A2%28a%2Bc%29%5E%7B-3%7D+%3D++frac%7B2%7D%7B%28a%2Bc%29%5E3%7D+ "а^{-3} = frac{1}{a^3} \ \
(5x)^{-2} = frac{1}{(5x)^2} = frac{1}{25x^2} \ \
xy^{-1} = x * frac{1}{y^1} = frac{x}{1} * frac{1}{y}= frac{x}{y} \ \
3m^2n^{-2} = 3m^2 * frac{1}{n^2} = frac{3m^2}{n^2} \ \
a^{-2} +b^{-2} = frac{1}{a^2} + frac{1}{b^2} = frac{b^2+a^2}{a^2b^2} \ \
(u-v)^{-2} = frac{1}{(u-v)^2} \ \
-10yz^{-19} =-10y * frac{1}{z^{19}} = - frac{10y}{z^{19}} \ \
2(a+c)^{-3} = frac{2}{(a+c)^3}")
№3.
![frac{2}{3^{-17}} = 2 : frac{1}{3^{17}} = 2 * frac{3^{17}}{1} = 2*3^{17} \ \
frac{a^{-2}}{b^{-3}} = frac{1}{a^2} : frac{1}{b^{3}} = frac{1}{a^2}* frac{b^3}{1} = frac{b^3}{a^2} \ \
frac{m}{np^{-2}} = frac{mp^2}{n} \ \
frac{ab}{(a+b)^{-2}} = frac{ab*(a+b)^2}{1} = ab(a+b)^2 \ \
frac{xy}{z^{-1}} = xyz^1 =xyz \ \
frac{z}{x^ny^{-k}} = frac{zy^k}{x^n}](https://tex.z-dn.net/?f=+frac%7B2%7D%7B3%5E%7B-17%7D%7D+%3D+2+%3A++frac%7B1%7D%7B3%5E%7B17%7D%7D++%3D+2+%2A++frac%7B3%5E%7B17%7D%7D%7B1%7D+%3D+2%2A3%5E%7B17%7D+%5C++%5C+%0A+frac%7Ba%5E%7B-2%7D%7D%7Bb%5E%7B-3%7D%7D+%3D++frac%7B1%7D%7Ba%5E2%7D+%3A++frac%7B1%7D%7Bb%5E%7B3%7D%7D+%3D++frac%7B1%7D%7Ba%5E2%7D%2A++frac%7Bb%5E3%7D%7B1%7D+%3D+frac%7Bb%5E3%7D%7Ba%5E2%7D++%5C++%5C+%0A+frac%7Bm%7D%7Bnp%5E%7B-2%7D%7D+%3D++frac%7Bmp%5E2%7D%7Bn%7D++%5C++%5C+%0A+frac%7Bab%7D%7B%28a%2Bb%29%5E%7B-2%7D%7D+%3D++frac%7Bab%2A%28a%2Bb%29%5E2%7D%7B1%7D+%3D+ab%28a%2Bb%29%5E2+%5C++%5C+%0A+frac%7Bxy%7D%7Bz%5E%7B-1%7D%7D+%3D+xyz%5E1+%3Dxyz+%5C++%5C+%0A+frac%7Bz%7D%7Bx%5Eny%5E%7B-k%7D%7D+%3D++frac%7Bzy%5Ek%7D%7Bx%5En%7D+ "frac{2}{3^{-17}} = 2 : frac{1}{3^{17}} = 2 * frac{3^{17}}{1} = 2*3^{17} \ \
frac{a^{-2}}{b^{-3}} = frac{1}{a^2} : frac{1}{b^{3}} = frac{1}{a^2}* frac{b^3}{1} = frac{b^3}{a^2} \ \
frac{m}{np^{-2}} = frac{mp^2}{n} \ \
frac{ab}{(a+b)^{-2}} = frac{ab*(a+b)^2}{1} = ab(a+b)^2 \ \
frac{xy}{z^{-1}} = xyz^1 =xyz \ \
frac{z}{x^ny^{-k}} = frac{zy^k}{x^n}")
№2.
№3.
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