Matematica

((10 - 5)^3 - 35/7)/(16^2/4^3)=

=(5^3 - 5)/(2^8/2^6)=

=(125 - 5)/4=120/4= 30

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((2^8)^2 + 2·(2^5)^3)/(1/2·(8^3)^2)=

=(2^16 + 2·2^15)/(1/2·(2^9)^2)=

=(2^16 + 2^16)/(1/2·2^18)=

=2·2^16/2^17=2^17/2^17 = 1

(10-5)^3-(35/7) = 125-5 = 120

(2^4)^2/(2^2)^3 = 2^8/2^6 = 2^2 = 4 

120/4 = 30 

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226)

$\small \dfrac{(10-5)^3-\dfrac{35}{7}}{\dfrac{16^2}{4^3} } = $

$\small =\dfrac{5^3-5}{\dfrac{4^2·4^2}{4^3} } = $

$\small =\dfrac{125-5}{\dfrac{4^{2+2}}{4^3} } = $

$\small =\dfrac{120}{\dfrac{4^4}{4^3} } = $

$\small =\dfrac{120}{4^{4-3} } = $

$\small =\dfrac{120}{4 } = 30$

227)

$\small \dfrac{(2^8)^2+2(2^5)^3}{\dfrac{1}{2}(8^3)^2 } = $

$\small = \dfrac{2^{8·2}+2·2^{5·3}}{\dfrac{1}{2}·8^{3·2}} = $

$\small = \dfrac{2^{16}+2·2^{15}}{2^{-1}·8^{6}} = $

$\small = \dfrac{2^{16}+2^{15+1}}{2^{-1}·(2^3)^6} = $

$\small = \dfrac{2^{16}+2^{16}}{2^{-1}·2^{3·6}} = $

$\small = \dfrac{2·2^{16}}{2^{-1}·2^{18}} = $

$\small = \dfrac{2^{1+16}}{2^{-1+18}} = $

$\small = \dfrac{2^{17}}{2^{17}} = $

$\small = \dfrac{\cancel{2^{17}}^1}{\cancel{2^{17}}_1} = 1$

2^16+2*(2^5)^3 = 2^16+2^16 = 2^(16+1) = 2^17

((2^3)^3)^2*2^-1 = 2^(18-1) = 2^17

2^17 / 2^17 = 1