Matematica

((121/11 - 2·(18 - 15))^2)^3/25^2 =

=((11 - 2·3)^2)^3/25^2=

=(5^2)^3/25^2=

=5^6/5^4=5^2 = 25

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4·2^4·(2^6)^2/((1/2·2^4)^2)^3=

=2^2·2^4·2^12/((2^3)^2)^3=

=2^18/(2^6)^3=

=2^18/2^18= 1

121/11-2(18-15) = 11-6 = 5

(5^2)^3 = 25^3

25^3/25^2 = 25^(3-2) = 25 

228)

$\small = \dfrac{\left\{\left[\dfrac{121}{11}-2(18-15)\right]^2\right\}^3}{25^2} = $

$\small = \dfrac{\left\{\left[11-2·3\right]^2\right\}^3}{5^2·5^2} = $

$\small = \dfrac{\left\{\left[11-6\right]^2\right\}^3}{5^{2+2}} = $

$\small = \dfrac{\left\{5^2\right\}^3}{5^4} = $

$\small = \dfrac{5^{2·3}}{5^4} = $

$\small = \dfrac{5^6}{5^4} = 5^{6-4} = 5^2 = 25$

2^4*2^2 = 2^6

2^6*2^12 = 2^(6+12) = 2^18

((2^4/2)^2)^3 = (2^6)^3 = 2^18

2^18 / 2^18 = 1 

229)

$\small = \dfrac{4·2^4·(2^6)^2}{\left[\left(\dfrac{2^4}{2}\right)^2\right]^3} = $

$\small = \dfrac{2^2·2^4·2^{6·2}}{\left[\left(2^{4-1}\right)^2\right]^3} = $

$\small = \dfrac{2^{2+4}·2^{12}}{\left[\left(2^3\right)^2\right]^3} = $

$\small = \dfrac{2^6·2^{12}}{2^{3·2·3}} = $

$\small = \dfrac{2^{6+12}}{2^{18}} = \dfrac{\cancel{2^{18}}^1}{\cancel{2^{18}}_1} = 1$