A expressão : quando escrita em base 2 , tem o expoente igual a :.... Pergunta de ideia deRafaelueno1

Rafaelueno1 @Rafaelueno1

January 2020 1 82 Report

A expressão :

$\frac{(0,5)^{-2} 2^{0,3333...} \sqrt[3]{6} }{(0,125)^{-3} }$

quando escrita em base 2 , tem o expoente igual a :

Lista de comentários

alevini $\mathsf{\frac{(0,5)^{-2}\cdot2^{0,333...}\cdot\sqrt[3]{16}}{(0,125)^{-3}}2^x}$

$\mathsf{\frac{\Big(\frac{1}{2}\Big)^{-2}\cdot2^{\frac{1}{3}}\cdot16^{\frac{1}{3}}}{\Big(\frac{1}{8}\Big)^{-3}}=2^x}$

$\mathsf{\frac{2^2\cdot2^{\frac{1}{3}}\cdot2^{\frac{4}{3}}}{8^3}=2^x}$

$\mathsf{\frac{2^{2+\frac{1}{3}+\frac{4}{3}}}{2^9}=2^x}$

$\mathsf{2^{\frac{11}{3}}\cdot2^{-9}=2^x}$

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

$\mathsf{2^{-\frac{16}{3}}=2^x}$

$\boxed{\mathsf{x=-\frac{16}{3}}}$

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