Question

4 elevado a -2 + 4 elevado a 2 -2 elevado a -1 / 2 elevado a -2 -2 elevado a -1​

Answer 1

Resposta:

Explicação passo-a-passo:

Temos que

$\frac{4^{-2}+4^{2}-2^{-1}}{2^{-2}-2^{-1}}=\frac{2^{-4}+2^{4}-2^{-1}}{2^{-2}-2^{-1}}=\frac{2^{-1}(2^{-3}+2^{5}-1)}{2^{-1}(2^{-1}-1)}=\frac{2^{-3}+2^{5}-1}{2^{-1}-1}=\frac{\frac{1}{2^{3}}+32-1}{\frac{1}{2}-1}=\frac{\frac{1}{8}+32-1}{\frac{1-2}{2}}=\frac{\frac{1+8.32-8.1}{8}}{-\frac{1}{2}}=\frac{\frac{1+256-8}{8}}{-\frac{1}{2}}=\frac{\frac{249}{8}}{-\frac{1}{2}}=\frac{249}{8}.(-\frac{2}{1}) =-\frac{249}{4}$