Oblicz wartość wyrażeń.



Oblicz Wartość Wyrażeń class=

Odpowiedź :

a)

[tex]\dfrac{5^{13}\cdot3+2\cdot5^{13}}{5^{11}:25^{4})\cdot25} = \dfrac{5^{13}(3+2)}{(5^{11}:(5^{2})^{4})\cdot5^{2}} = \dfrac{5^{13}\cdot5}{(5^{11}:5^{8})\cdot5^{2}} =\dfrac{5^{14}}{5^{3}\cdot5^{2}} =\dfrac{5^{14}}{5^{5}} =\\\\= 5^{9} = 1953125[/tex]

b)

[tex]2^{\frac{1}{2}}\cdot50^{\frac{1}{2}}-2^{\frac{1}{5}}\cdot16^{\frac{1}{5}}=(2\cdot50)^{\frac{1}{2}} -(2\cdot16})^{\frac{1}{5}} = 100^{\frac{1}{2}}-32^{\frac{1}{5}}=(10^{2})^{\frac{1}{2}}-(2^{5})^{\frac{1}{5}}=\\\\=10-2 = 8[/tex]