Question

Calcule o valor da expressão $\left(-3\right)^2+\left(1/2\right)^{-2}-\left(2/5\right)^2\:\div -2^4+\left(-1\right)^2+5^0-\left(3/4\right)^{-2}$

a. 1161/3552
b. -3550/1161
c. 3550/1161
d. -1161/3550

Answer 1

Resolvendo:

$\mathsf{=\dfrac{-3^2+\left(\frac{1}{2}\right)^{-2}-\left(\frac{2}{5}\right)^2}{-2^4+\left(-1\right)^2+5^0-\left(\frac{3}{4}\right)^{-2}}}\\\\\\\mathsf{=\dfrac{-9+2^2-\frac{2^2}{5^2}}{-16+1+1-\left(\frac{4}{3}\right)^2}}\\\\\\\mathsf{=\dfrac{-9+4-\frac{4}{25}}{-16+2-\frac{4^2}{3^2}}}\\\\\\\mathsf{=\dfrac{-5-\frac{4}{25}}{-14-\frac{16}{9}}}\\\\\\\mathsf{=\dfrac{\frac{-5\cdot 25}{25}-\frac{4}{25}}{\frac{-14\cdot 9}{9}-\frac{16}{9}}}\\\\\\\mathsf{=\dfrac{\frac{-125-4}{25}}{\frac{-126-16}{9}}}\\\\\\\mathsf{=\dfrac{\frac{-129}{25}}{\frac{-126}{9}}}\\\\\\\mathsf{=\dfrac{129}{25}\cdot \dfrac{9}{126}}\\\\\\\mathsf{=\boxed{\dfrac{1161}{3550}}}\: \: \checkmark$

= = = = =

Resposta: Letra A