Question

1ª ) Simplifique a expressão: 2^98- 4 ^50 : 2 ^99 - 2 ^101:

Answer 1

$\boxed{ \frac{2^{99}-4^{50}}{2^{98}-2^{101}}}$

reescrevendo
4 = 2²
e colocando 2^98 em evidencia

$\frac{2^{99}-(2^2)^{50}}{2^{98}-2^{101}}\\\\= \frac{2^{99}-2^{100}}{2^{98}-2^{101}}\\\\ = \frac{2^{98}*(2^{(99-98)} -2^{(100-98)}}{2^{98}*(2^{(98-98)}-2^{(101-98)})} \\\\= \frac{2^1 - 2^2}{2^0-2^3} \\\\= \frac{2-4}{1-8}= \frac{-2}{-7}= \boxed{ \frac{2}{7} }$