Espressioni n 261

((2/9)^4·(3/14)^4)^2/((- 1/7)^2)^4·((- 5/6)^3/(5/18)^3)^3=

=(2^4/3^8·(3/14)^4)^2/((- 1/7)^2)^4·((- 5/6)^3/(5/18)^3)^3=

=(2^4/3^8·(3^4/(2^4·7^4)))^2/(1/7^8)·((- 5^3/(2^3·3^3))/(5^3/(2^3·3^6)))^3=

=(1/(3^4·7^4))^2/(1/7^8)·(- 3^3)^3=

=1/(3^8·7^8)/(1/7^8)·(- 3^3)^3=

=1/(3^8·7^8)/(1/7^8)·(- 3^9)=

=1/3^8·(- 3^9)= 

=-3

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$\small \left\{\left[\left(\dfrac{2}{9}\right)^4·\left(\dfrac{3}{14}\right)^4\right]^2÷\left[\left(-\dfrac{1}{7}\right)^2\right]^4\right\}·\left[\left(-\dfrac{5}{6}\right)^3÷\left(\dfrac{5}{18}\right)^3\right]^3 =$

$\small = \left\{\left[\left(\dfrac{\cancel2^1·\cancel3^1}{\cancel9_3·\cancel{14}_7}\right)^4\right]^2÷\left(-\dfrac{1}{7}\right)^{2·4}\right\}·\left[\left(-\dfrac{\cancel5^1}{\cancel6_1}·\dfrac{\cancel{18}^3}{\cancel5_1}\right)^3\right]^3 =$

$\small = \left\{\left[\left(\dfrac{1}{21}\right)^4\right]^2÷\left(-\dfrac{1}{7}\right)^8\right\}·\left[\left(-1·3\right)^3\right]^3 =$

$\small = \left\{\left(\dfrac{1}{21}\right)^{4·2}·\left(-7\right)^8\right\}·\left(-3\right)^{3·3} =$

$\small = \left\{\left(\dfrac{1}{21}\right)^8·\left(-7\right)^8\right\}·\left(-3\right)^9 =$

$\small = \left\{\left(\dfrac{1}{\cancel{21}_3}·-\cancel7^1\right)^8\right\}·\left(-3\right)^9 =$

$\small = \left\{\left(\dfrac{1}{3}·-1\right)^8\right\}·\left(-3\right)^9 =$

$\small = \left(-\dfrac{1}{3}\right)^8·\left(-3\right)^9 =$

$\small = \dfrac{1}{\cancel{6561}_1}·-\cancel{19683}^3 =$

$\small = \dfrac{1}{1}·-3 =$

$\small = -3 $

{[(2/9)^4 * (3/14)^4]^2 : [(- 1/7)^2]^4} * [(- 5/6)^3 : (5/18)^3]^3 =

Potenze con lo stesso esponente 2/9 e 3/14, si moltiplicano le basi poi si eleva a 4 * 2 = 8: 

 [(2/9 * 3/14)^4]^2 = [(1/3 * 1/7)^4]^2 = (1/21)^8;

{(1/21)^8 : (- 1/7)^8} * [(- 5/6 * 18/5)^3]^3 =

= { [(1/21) * (- 7/1)]^8 } * [(- 3/1)]^9 =

= {- 1/3}^8 * (- 3/1)^9 =

= (- 1/3)^8 * (- 3/1)^9 =

= (+ 1/3)^8 * (- 3/1)^9 =

= + 1/(3)^8 * (-3)^9  =

= (-3)^9 : 3^8 = 

= - 3^1 = - 3.

Ciao  @eliacangi

fai venire il torcicollo.