[tex]a)\\\\\dfrac{64^{4}\div (4+4+4+4)}{16^{3} \cdot 4} =\dfrac{64^{4}\div (16)}{(4^{2} )^{3} \cdot 4} =\dfrac{(4^{3} )^{4} \div 4^{2} }{4^{6} \cdot 4} =\dfrac{4^{12} \div 4^{2} }{4^{7} } =\dfrac{4^{10} }{4^{7} } =4^{10-7} =4^{3}[/tex]
[tex]\dfrac{(27^{4} \div 9^{5} \cdot (3^{8} \div \frac{1}{27} ))}{\frac{1}{9} \cdot 81^{2} } =\dfrac{((3^{3} )^{4} \div (3^{2} )^{5} \cdot (3^{8} \div 27^{-1} ))}{9^{-1} \cdot (3^{4} )^{2} } =\dfrac{(3^{12} \div 3^{10} \cdot (3^{8} \div 3^{-3} ))}{3^{-2} \cdot 3^{8} } =\dfrac{(3^{12} \div 3^{10} \cdot 3^{11} )}{3^{6} } =\dfrac{(3^{2} \cdot 3^{11} )}{3^{6} }=\dfrac{3^{13} }{3^{6} } =3^{13-6} =3^{7}[/tex]
korzystam zw wzorów:
[tex]x^{n} \cdot x^{m} =x^{n+m} \\\\x^{n} \div x^{m} =x^{n-m} \\\\(x^{n} )^{m} =x^{n\cdot m}\\\\\dfrac{x}{y} =(\dfrac{y}{x}) ^{-1}[/tex]
