espressione 294

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294)

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

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

$\small =\left[\left(-\dfrac{1}{4}\right)^5\right]^2 · \left[\left(-\dfrac{1}{4}\right)^{10}\right]^{-1}=$

$\small =\left(-\dfrac{1}{4}\right)^{5·2} · \left(-\dfrac{1}{4}\right)^{10·(-1)}=$

$\small =\left(-\dfrac{1}{4}\right)^{10} · \left(-\dfrac{1}{4}\right)^{-10}=$

$\small =\left(-\dfrac{1}{4}\right)^{10+(-10)}=$

$\small =\left(-\dfrac{1}{4}\right)^{10-10}=$

$\small =\left(-\dfrac{1}{4}\right)^0= 1$