Úprava výrazů pro t, x, y, z
Uprav výrazy pro t, x, y, z ≠ 0:
\( \large \left[ {\left( {\Large \frac{{{x^{2}}y}}{{{t^{2}}z}}\large } \right) ^{ - 1}}:{\left( {\Large \frac{{xy}}{{zt}}\large } \right) ^{ - 2}}\right] \cdot \Large \frac{z}{y}\large \)
\( \large = {t^{-2}} \cdot {z^{-2}} \cdot {x^{-2}} \cdot {y^{-2}} = {t^{-4}} \cdot {z^{-4}} \cdot {x^{-4}} \cdot {y^{-4}} = \frac{1}{t^4z^4x^4y^4} \)
\( \large = {t^{1}} \cdot {z^{1}} \cdot {x^{1}} \cdot {y^{1}} = {t} \cdot {z} \cdot {x} \cdot {y} = tzyx \)
\( \large = {t^{2}} \cdot {z^{2}} \cdot {x^{2}} \cdot {y^{2}} = {t^{4}} \cdot {z^{4}} \cdot {x^{4}} \cdot {y^{4}} = 16 \cdot 16 \cdot 16 \cdot 16 = 65536 \)
\( \large = {t^{2-2}} \cdot {z^{2-2}} \cdot {x^{2-2}} \cdot {y^{2-2}} = {t^{0}} \cdot {z^{0}} \cdot {x^{0}} \cdot {y^{0}} = 1 \cdot 1 \cdot 1 \cdot 1 = 1 \)