[tex]a)\\\\\dfrac{5^{8} \cdot 5^{0} \cdot 5 }{5^{7} } =\dfrac{5^{8} \cdot 1\cdot 5^{1} }{5^{7} } =\dfrac{5^{8+1} }{5^{7} } =\dfrac{5^{9} }{5^{7} } =5^{9-7} =5^{2}[/tex]
[tex]b)\\\\0,5^{5} \cdot ((0,5)^{3}) ^{2} \div 0,5^{4} =0,5^{5} \cdot 0,5^{3\cdot 2 } \div 0,5^{4} =0,5^{5} \cdot 0,5^{6 } \div 0,5^{4}=0,5^{5+6 } \div 0,5^{4}=0,5^{11 } \div 0,5^{4}=0,5^{11-4 } =0,5^{7}[/tex]
[tex]c)\\\\\dfrac{(a^{2} )^{3} \cdot a^{0} \cdot a^{6} }{a^{10} \div a^{6} } =\dfrac{a^{2\cdot 3} \cdot 1 \cdot a^{6} }{a^{10-6}} =\dfrac{a^{6}\cdot a^{6} }{a^{4} } =\dfrac{a^{6+6} }{a^{4} } =\dfrac{a^{12} }{a^{4} } =a^{12-4} =a^{8}[/tex]
[tex]d)\\\\\dfrac{(x^{0} )^{7} \cdot (x^{17} )^{0} }{( (x^{17} )^{2} \div x^{17} )^{0} } =\dfrac{1^{7} \cdot x^{0} }{ (x^{17\cdot 2} \div x^{17}) ^{0} } =\dfrac{1\cdot 1 }{ (x^{34} \div x^{17}) ^{0} } =\dfrac{1}{ ( x^{34-17}) ^{0} } =\dfrac{1}{ ( x^{17}) ^{0} } =\dfrac{1}{1} =1[/tex]
Korzystam ze wzorów:
[tex]x^{n} \cdot x^{m} =x^{n+m} \\\\x^{n} \div x^{m} =\dfrac{x^{n} }{x^{m} } =x^{n-m} \\\\x^{0} =1\\\\(x^{n} )^{m} =x^{n\cdot m}[/tex]
