Question

Qual o valor da numerico da expressao a.b.(a^-1.b³)².(a.b^-1)^5/a.b^-3.(a².b)⁴.a^-6.b^-1. me ajudem por favor

Answer 1

Olá.

$\dfrac{a\cdot b\cdot(a^{-1}\cdot b^3)^2\cdot(a\cdot b^{-1})^5}{a\cdot b^{-3}\cdot(a^2\cdot b)^4\cdot a^{-6}\cdot b^{-1}}\\\\\\\dfrac{20\cdot(-4)\cdot(20^{-1}\cdot (-4)^3)^2\cdot(20\cdot (-4)^{-1})^5}{20\cdot (-4)^{-3}\cdot(20^2\cdot(-4))^4\cdot 20^{-6}\cdot(-4)^{-1}}=\\\\\\\dfrac{-80\cdot(\dfrac{1}{20}\cdot(-64))^2\cdot(20\cdot\dfrac{1}{-4})^5}{20\cdot\dfrac{1}{-64}\cdot(400\cdot\dfrac{1}{-64})^4\cdot\dfrac{1}{64000000}\cdot\dfrac{1}{-4}}=$
$\dfrac{-80\cdot(\dfrac{-64}{20})^2\cdot(\dfrac{20}{-4})^5}{\dfrac{20}{-64}\cdot(\dfrac{400}{-64})^4\cdot\dfrac{1}{-256000000}}=\\\\\\ \dfrac{-80\cdot(\dfrac{4096}{400})\cdot(\dfrac{3200000}{-1024})}{\dfrac{20}{-64}\cdot(\dfrac{25600000000}{16777216})\cdot\dfrac{1}{-256000000}}$
$\dfrac{-80\cdot(\dfrac{4096}{400})\cdot(\dfrac{3200000}{-1024})}{\dfrac{20}{-64}\cdot(\dfrac{25600000000}{16777216})\cdot\dfrac{1}{-256000000}} \\\\\\\\ \dfrac{\dfrac{-80\cdot4096\cdot3200000}{400\cdot(-1024)}}{\dfrac{20\cdot25600000000\cdot1}{-64\cdot16777216\cdot-25600000000}}=\\\\\\\dfrac{\dfrac{-1048576000000}{-409600}}{\dfrac{512000000000}{27487790694400000000}}$

Cortando os zeros e continuando...

$\dfrac{\dfrac{-10485760000}{-4096}}{\dfrac{5120}{274877906944}}=\\\\\\\dfrac{-10485760000}{-4096}\cdot\dfrac{274877906944}{5120}=\\\\\\ \dfrac{-2882303761517117440000}{-20971520}=\\\\\\\boxed{\boxed{\boxed{137.438.953.472.000}}}$

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Bons estudos.