simplifique cada uma das expressões apresentadas a seguir:
a)³√32•2^-⅔•(⅔)^0
b)4^10•8^-3•-2 elevado a 32
Soluções para a tarefa
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2
Olá.
a)
![(
\sqrt[3]{32}).(2^{-\frac{2}{3}}).(\frac{2}{3})^0\\\\
(\sqrt[3]{2^3.2}).(2^{-\frac{2}{3}}).1\\\\
2.(\sqrt[3]{2}).(2^{-\frac{2}{3}})\\\\ 2^1.2^{\frac{1}{3}}.2^{-\frac{2}{3}}
\longrightarrow 1+\frac{1}{3}-\frac{2}{3}} = \frac{3+1-2}{3} = \frac{2}{3}\\\\
2^{\frac{2}{3}} (
\sqrt[3]{32}).(2^{-\frac{2}{3}}).(\frac{2}{3})^0\\\\
(\sqrt[3]{2^3.2}).(2^{-\frac{2}{3}}).1\\\\
2.(\sqrt[3]{2}).(2^{-\frac{2}{3}})\\\\ 2^1.2^{\frac{1}{3}}.2^{-\frac{2}{3}}
\longrightarrow 1+\frac{1}{3}-\frac{2}{3}} = \frac{3+1-2}{3} = \frac{2}{3}\\\\
2^{\frac{2}{3}}](https://tex.z-dn.net/?f=%28%0A%5Csqrt%5B3%5D%7B32%7D%29.%282%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%29.%28%5Cfrac%7B2%7D%7B3%7D%29%5E0%5C%5C%5C%5C%0A%28%5Csqrt%5B3%5D%7B2%5E3.2%7D%29.%282%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%29.1%5C%5C%5C%5C%0A2.%28%5Csqrt%5B3%5D%7B2%7D%29.%282%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%29%5C%5C%5C%5C+2%5E1.2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D.2%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%0A%5Clongrightarrow+1%2B%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B2%7D%7B3%7D%7D+%3D+%5Cfrac%7B3%2B1-2%7D%7B3%7D+%3D+%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5C%0A2%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D)
b)
![\frac{4^{10}.8^{-3}.(-2)}{32} \\\\
\longrightarrow 4 = 2^2\\ \longrightarrow 8 = 2^3\\ \longrightarrow 32 = 2^5\\\\
\frac{(2^2)^{10}.(2^3)^{-3}.(-2)}{2^5}\\\\
\frac{2^{20}.2^{-9}.(-2)}{2^5}\\\\
\frac{2^{11}.(-2)}{2^5}\\\\
2^{11-5}.(-2)\\\\
2^{6}.(-2^1)\\\\
(-2)^7 \frac{4^{10}.8^{-3}.(-2)}{32} \\\\
\longrightarrow 4 = 2^2\\ \longrightarrow 8 = 2^3\\ \longrightarrow 32 = 2^5\\\\
\frac{(2^2)^{10}.(2^3)^{-3}.(-2)}{2^5}\\\\
\frac{2^{20}.2^{-9}.(-2)}{2^5}\\\\
\frac{2^{11}.(-2)}{2^5}\\\\
2^{11-5}.(-2)\\\\
2^{6}.(-2^1)\\\\
(-2)^7](https://tex.z-dn.net/?f=%5Cfrac%7B4%5E%7B10%7D.8%5E%7B-3%7D.%28-2%29%7D%7B32%7D+%5C%5C%5C%5C+%0A%5Clongrightarrow+4+%3D+2%5E2%5C%5C+%5Clongrightarrow+8+%3D+2%5E3%5C%5C+%5Clongrightarrow+32+%3D+2%5E5%5C%5C%5C%5C%0A%5Cfrac%7B%282%5E2%29%5E%7B10%7D.%282%5E3%29%5E%7B-3%7D.%28-2%29%7D%7B2%5E5%7D%5C%5C%5C%5C%0A%5Cfrac%7B2%5E%7B20%7D.2%5E%7B-9%7D.%28-2%29%7D%7B2%5E5%7D%5C%5C%5C%5C%0A%5Cfrac%7B2%5E%7B11%7D.%28-2%29%7D%7B2%5E5%7D%5C%5C%5C%5C%0A2%5E%7B11-5%7D.%28-2%29%5C%5C%5C%5C%0A2%5E%7B6%7D.%28-2%5E1%29%5C%5C%5C%5C%0A%28-2%29%5E7)
Espero ter ajudado. Qualquer dúvida comenta aí.
a)
b)
Espero ter ajudado. Qualquer dúvida comenta aí.
richardsilva77p9r6jt:
mas se vc nao puder fazer tudo bem,eu errei na hora de digitar
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