Question

Решите, по теме Степени!

Answer 1

$1)\frac{3^{6,5}}{9^{2,25}}=\frac{3^{6,5}}{(3^{2})^{2,25}}=\frac{3^{6,5}}{3^{4,5}}=3^{6,5-4,5}=3^{2}=9\\\\Otvet:\boxed{9}$

$2)\frac{4^{2}*12^{3}*9}{32*3^{4}}=\frac{(2^{2})^{2}*(2^{2}*3)^{3}*3^{2}}{2^{5}*3^{4}}=\frac{2^{4}*2^{6}*3^{3}*3^{2}}{2^{5}*3^{4}}=2^{4+6-5}*3^{3+2-4}=2^{5}*3=32*3=96\\\\Otvet:\boxed{96}$

$3)7^{-1}*(\frac{1}{49})^{-1}+2^{-1}*2^{2}=\frac{1}{7}*49+\frac{1}{2}*4=7+2=9\\\\Otvet:\boxed{9}$

$4)\frac{8^{\frac{1}{3}}*25^{\frac{1}{2}}-2}{64^{\frac{1}{3}}}=\frac{(2^{3})^{\frac{1}{3}}*(5^{2})^{\frac{1}{2}}-2}{(4^{3})^{\frac{1}{3}}}=\frac{2*5-2}{4}=\frac{8}{4}=2\\\\Otvet:\boxed{2}$