Найдите значение выражения
23−72⋅87232^{3-7\sqrt {2}} \cdot 8^{7\sqrt {2} \over 3}23−72⋅8372
Какими формулами мы пользуемся?
an=a1n;(an)m=an⋅m\displaystyle { \sqrt [n] a = a^{ \frac {1} {n} }; (a^n)^m = a^{n \cdot m} }na=an1;(an)m=an⋅m
23−72⋅8723=23−72⋅22723=23−72⋅22⋅7232^{3-7\sqrt {2}} \cdot 8^{7\sqrt {2} \over 3} = 2^{3-7\sqrt {2}} \cdot 2^{2^{7\sqrt {2} \over 3}} = 2^{3-7\sqrt {2}} \cdot 2^{2 \cdot{7\sqrt {2} \over 3}}an⋅am=aa+m\displaystyle { a^n \cdot a^m = a^{a+m} }an⋅am=aa+m
axay=ax−y\displaystyle{\frac{a^x}{a^y}} = a^{x-y}ayax=ax−y
8=2∗2∗2=238=2*2*2=2^38=2∗2∗2=23
23−72⋅8723=23−72⋅23723=23−72⋅23⋅723=2^{3-7\sqrt {2}} \cdot 8^{7\sqrt {2} \over 3} = 2^{3-7\sqrt {2}} \cdot 2^{3^{7\sqrt {2} \over 3} } = 2^{3-7\sqrt {2}} \cdot 2^{3\cdot {7\sqrt {2} \over 3} } = 23−72⋅8372=23−72⋅23372=23−72⋅23⋅372=
23−72⋅272=23−72+72=23=82^{3-7\sqrt {2}} \cdot 2^{ {7 \sqrt {2} } } = 2^{3-7\sqrt {2} + {7\sqrt {2} } } = 2^3 = 823−72⋅272=23−72+72=23=8