Question

Se p =2^3^2, q=(4^2)^3, r=8^2^3 e s=(pq/r)^1/3,
então se pode afirmar que:
a)0<s<1/4 
b)0<s<1/2
c)0 <s<1
d)1 <s<2
e)2<s<4

Answer 1

vamos  calcular os valores separados para facilitar

$p= 2^{3 ^{2} } =2^9 \\ \\ q=(4^2)^3=4^6=(2^2)^6=2^{12} \\ \\ r=8^{2^3} =8^8=(2^3)^8=2^{24} \\ \\ logo \\ \\ ( \frac{p.q}{r} )^{ \frac{1}{3}} = \\ \\ ( \frac{2^9.2^{12}}{2^{24}} )^{ \frac{1}{3}} = \\ \\ ( \frac{2^{9+12}}{2^{24}} )^ \frac{1}{3} = \\ \\ (2^{21}\div2^{24})^{ \frac{1}{3} } \\ \\ (2^{21-24})^{ \frac{1}{3}} = \\ \\ (2^{-3})^ \frac{1}{3} = \\ \\ 2^{- \frac{3}{3}} =2^{-1}= \frac{1}{2} \\ \\ R\mapsto0\ \textless \ s\ \textless \ 1$

Answer 2

Resposta: Letra c)

Explicação passo-a-passo: