Wykonaj wskazane działania i podaj wynik w postaci potęgi liczby 3.... Question from @LynxLynx

October 2018 2 23 Report

Wykonaj wskazane działania i podaj wynik w postaci potęgi liczby 3

$\frac{9^{\frac{21}{2}}\cdot(\frac{1}{81})^{21/4}:\sqrt[6]{27^2} }{5\cdot3^\frac{7}{2}-6\cdot3\frac{5}{2}}$

$\frac{9^{\frac{21}{2}}\cdot(\frac{1}{81})^{\frac{21}{4}}:\sqrt[6]{27^2}}{5\cdot3^{\frac{7}{2}}-6\cdot3^{\frac{5}{2}}}=$

$=\frac{(3^2)^{\frac{21}{2}}\cdot(3^{-4})^{\frac{21}{4}}:((3^3)^2)^{\frac{1}{6}}}{5\cdot3^{\frac{7}{2}}-2\cdot3\cdot3^{\frac{5}{2}}}=$

$=\frac{3^{21}\cdot3^{-21}:3^1}{5\cdot3^{\frac{7}{2}}-2\cdot3^{\frac{7}{2}}}=$

$=\frac{3^0:3^1}{3\cdot3^{\frac{7}{2}}}=\frac{3^{-1}}{3^{\frac{9}{2}}}=$

$=3^{-1-\frac{9}{2}}=3^{-\frac{11}{2}}$

1 votes Thanks 1

lapik

$\frac{9^{10,5}\cdot(\frac{1}{81})^{5,25}:\sqrt[6]{27^{2}}}{5\cdot3^{3,5}-6\cdot3^{2,5}}=\frac{3^{21}\cdot3^{-21}:3^{1}}{5\cdot3^{3,5}-2\cdot3^{3,5}}=\frac{3^{-1}}{3\cdot3^{3,5}}=\frac{3^{-1}}{3^{4,5}}=3^{-5,5}$

1 votes Thanks 1

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