N° 52

(6^3 x 6^5 x 2^8) ÷ (3^5 x 4^5 ÷ 15^4)^8 + [(7^0)^3]^5 x (3^2 x 2^0 ÷ 3) =

(6^8 x 2^8) : [(3^5 x 4^5) ÷ (3^4 x 5^4)]^8 + [1^3]^5 x (9 x 1 : 3) =

(12^8) : [(3 x 4^5) : (5^4)]^8  + 1 x  3 =

{(3 x 4) : [(3 x 4^5) : (5^4)]}^8 + 3=

= [3 x 4 x 5^4 : (3 x 4^5)]^8 + 3 =

= [5^4 : 4^4]^8  + 3 =

= (5/4)^4]^8 + 3 =

(5/4)^32 + 3 ....

$\small (6^3 ·6^5 · 2^8) ÷ (3^5 · 4^5 ÷ 15^4)^8 + [(7^0)^3]^5 · (3^2 · 2^0 ÷ 3)$

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$\small \dfrac{6^3·6^5·2^8}{\left(\dfrac{3^5·4^5}{15^4}\right)^8}+\left[\left(7^0\right)^3\right]^5·\left(\dfrac{3^2·2^0}{3}\right)=$

$\small = \dfrac{6^{3+5}·2^8}{\left(\dfrac{(3·4)^5}{15^4}\right)^8}+\left[1^3\right]^5·\left(\dfrac{\cancel9^3·1}{\cancel3_1}\right)=$

$\small = \dfrac{6^8·2^8}{\left(\dfrac{12^5}{15^4}\right)^8}+1^{3·5}·3=$

$\small = \dfrac{12^8}{\left(\dfrac{3^{\cancel5^1}·4^5}{3^{\cancel4}·5^4}\right)^8}+1^8·3=$

$\small = \dfrac{12^8}{\left(3·\dfrac{4^5}{5^4}\right)^8}+1·3=$

$\small = \dfrac{\cancel{3^8}·4^8}{\cancel{3^8}·\dfrac{4^{5·8}}{5^{4·8}}}+1·3=$

$\small = \dfrac{4^8}{\dfrac{4^{40}}{5^{32}}}+3=$

$\small = 4^8·4^{-40}·5^{32}+3=$

$\small = 4^{8-40}·5^{32}+3=$

$\small = 4^{-32}·5^{32}+3=$

$\small = \left(\dfrac{1}{4}\right)^{32}·5^{32}+3=$

$\small = \left(\dfrac{1}{4}·5\right)^{32}+3=$

$\small = \left(\dfrac{5}{4}\right)^{32}+3=$

$\small = 1262,177448+3= 1265,177448$

$\small\text{S.E.\&O. miei o nel testo della domanda.}$