Question

Represente com uma única potência:


A) √32.2^0.5/2^-8

B)3^-4.3^11/27

Answer 1

Resposta:

A)

${\sqrt{32} .2^{0,5}\over2^{-8}}=\\ \\ 0,5\mapsto{5\over10}={1\over2}\\ \\ \sqrt{32} =\sqrt{2^5} =2^{5\over2}}\\ \\ logo\\ \\{ 2^{5\over2}.2^{1\over2}\over2^{-8}}=\\ \\ {2^{{5\over2}+{1\over2}}\over2^{-8}}=2^3\div2^{-8}=2^{3-(-8)}=2^{3+8}=\fbox{ 3^{11} }$

B)

${3^{-4}.3^{11}\over27}=\\ \\ {3^{-4+11}\over3^3}=\\ \\ 3^7\div3^3=3^{7-3}=\fbox{ 3^4 }$