[Risolto] 309 Chiedo aiuto (numeri razionali e reali)

309)

$\small \left\{\left(\dfrac{16}{5}\right)^3 : \left[\left(\dfrac{8}{5}\right)^2\right]^{-1}·\left(\dfrac{4}{5}-4\right)^{-4}\right\}^3·\left(-\dfrac{2}{5}\right)^{-1} : \left(-\dfrac{4}{5}\right)^4=$

$\small =\left\{\left(\dfrac{16}{5}\right)^3 : \left(\dfrac{5}{8}\right)^2·\left(\dfrac{4-20}{5}\right)^{-4}\right\}^3·-\dfrac{5}{2}·\left(-\dfrac{5}{4}\right)^4=$

$\small =\left\{\dfrac{16^3}{5^3} : \dfrac{25}{64}·\left(-\dfrac{16}{5}\right)^{-4}\right\}^3·-\dfrac{5}{2}·\left(-\dfrac{5}{4}\right)^4=$

$\small =\left\{\dfrac{16^3}{5^3}·\dfrac{64}{25}·\left(-\dfrac{5}{16}\right)^4\right\}^3·-\dfrac{5}{2}·\left(-\dfrac{5}{4}\right)^4=$

$\small =\left\{\dfrac{16^3}{5^3}·\dfrac{64}{25}·-\dfrac{5^4}{16^4}\right\}^3·-\dfrac{5}{2}·-\dfrac{5^4}{4^4}=$

$\small =\left\{\dfrac{\cancel{16^3}^1}{\cancel{5^3}_1}·\dfrac{64}{25} · -\dfrac{5^{\cancel4^1}}{16^{\cancel4^1}}\right\}^3 · -\dfrac{5}{2} · -\dfrac{5^4}{4^4}=$

$\small =\left\{\dfrac{1}{1}·\dfrac{64}{25} · -\dfrac{5}{16}\right\}^3 · -\dfrac{5}{2} · -\dfrac{5^4}{4^4}=$

$\small =\left\{\dfrac{1}{1}·\dfrac{\cancel{64}^4}{\cancel{25}_5} · -\dfrac{\cancel5^1}{\cancel{16}_1}\right\}^3 · -\dfrac{5}{2} · -\dfrac{5^4}{4^4}=$

$\small =\left\{\dfrac{4}{5} · -\dfrac{1}{1}\right\}^3 · -\dfrac{5}{2} · -\dfrac{5^4}{4^4}=$

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

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

$\small = -\dfrac{\cancel{4^3}^1}{\cancel{5^3}^1} · -\dfrac{5}{2} · -\dfrac{5^{\cancel4^1}}{4^{\cancel4^1}}=$

$\small = -\dfrac{1}{1} · -\dfrac{5}{2} · -\dfrac{5}{4}= -\dfrac{25}{8}$

((16/5)^3/((8/5)^2)^(-1)·(4/5 - 4)^(-4))^3·(- 2/5)^(-1)/(- 4/5)^4=

=((2^4/5)^3/((8/5)^2)^(-1)·(- 16/5)^(-4))^3·(- 2/5)^(-1)/(- 4/5)^4=

=((2^4/5)^3/(2^6/5^2)^(-1)·(5^4/2^16))^3·(- 2/5)^(-1)/(2^8/5^4)=

=((2^4/5)^3/(2^6/5^2)^(-1)·(5^4/2^16))^3·(- 5/2)/(2^8/5^4)=

=(2^12/5^3/(5^2/2^6)·(5^4/2^16))^3·(- 5/2)/(2^8/5^4)=

=(2^2/5)^3·(- 5/2)/(2^8/5^4)=

=2^6/5^3·(- 5/2)/(2^8/5^4)=

=(- 2^5/5^2)/(2^8/5^4)=

=- 5^2/2^3= - 25/8