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Esercizio 264

81^3 = (3^4)^3 = 3^12;

27^8 = (3^3)^8 = 3^24;

9^8= (3^2)^8 = 3^16

3^12 × 3^24 × 3^16 = 3^52;

3^52 :3^51 = 3^1 = 3;

18^12 = (3^2 × 2)^12 = 3^24 × 2^12;

12^8 = (3 × 2^2)^8 = 3^8 × 2^16;

24^9 = (3 × 2^3)^9  = 3^9 × 2^27;

3^12 * 3^24 * 3^16 : 3^51  = 3^1;

3^1 - (3^24 * 2^12) : 3^23 * (3^8 * 2^16) : (3^9 × 2^27) =

= 3 - 3^1 * 2^12 * 3^8 * 2^16 : (3^9 * 2^27) =

= 3 - 3^9 * 2^28 : 3^9 : 2^27=

= 3 - 3^0 * 2^1 = 

= 3 - 1 * 2 =

= 3 - 2 = 1.

Ciao  @eliacangi

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$\small 81^3·27^8·9^8 : 3^{51}-18^{12} : 3^{23}·12^8 : 24^9$

$\small \dfrac{(3^4)^3·(3^3)^8·(3^2)^8}{3^{51}}-\dfrac{2^{12}·(3^2)^{12}}{3^{23}}·(2^2)^8·3^8 : 24^9$

$\small \dfrac{3^{4·3}·3^{3·8}·3^{2·8}}{3^{51}}-\dfrac{2^{12}·3^{2·12}}{3^{23}}·2^{2·8}·3^8 : 24^9$

$\small \dfrac{3^{12}·3^{24}·3^{16}}{3^{51}}-\dfrac{2^{12}·3^{24}}{3^{23}}·2^{16}·3^8 : 24^9$

$\small \dfrac{3^{12+24+16}}{3^{51}}-2^{12}·3^{24-23}·2^{16}·3^8 : 24^9$

$\small \dfrac{3^{52}}{3^{51}}-2^{12}·3^1·2^{16}·3^8 : 24^9$

$\small 3^{52-51}-2^{12+16}·3^{1+8} : 24^9$

$\small 3^1-2^{28}·3^9 : 24^9$

$\small 3-\dfrac{2^{28}·3^9}{24^9}$

$\small 3-\dfrac{2^{28}·3^9}{(2^3)^9·3^9}$

$\small 3-\dfrac{2^{28}·\cancel{3^9}}{2^{3·9}·\cancel{3^9}}$

$\small 3-\dfrac{2^{28}}{2^{27}}$

$\small 3-2^{28-27}$

$\small 3-2^1$

$\small 3-2 = 1$