8.16. Вычислите: а) (1/4)^(−1/2) · 25^(1/2) − 81^(1/2) · 125^(−1/3); б) 49^(−1/2) · (1/7)^(−2) + 2^(−1) · (−2)^(−2); в) 216^(−1/3) · (1/6)^(−2) − 5^(−1) · (1/25)^(−1/2); г) (1/4)^(−1/2) · 16^(1/2) − 2^(−1) · (1/25)^(−1/2) · 8^(−1/3).

Question

Вопрос:

Accepted Answer

\(\left(\frac14\right)^{-1/2}·25^{1/2}-81^{1/2}·125^{-1/3}=2·5-9·\frac15=10-\frac95=\frac{41}{5}\).
\(49^{-1/2}·\left(\frac17\right)^{-2}+2^{-1}·(-2)^{-2}=\frac17·49+\frac12·\frac14=7+\frac18=\frac{57}{8}\).
\(216^{-1/3}·\left(\frac16\right)^{-2}-5^{-1}·\left(\frac1{25}\right)^{-1/2}=\frac16·36-\frac15·5=6-1=5\).
\(\left(\frac14\right)^{-1/2}·16^{1/2}-2^{-1}·\left(\frac1{25}\right)^{-1/2}·8^{-1/3}=2·4-\frac12·5·\frac12=8-\frac54=\frac{27}{4}\).

Ответ: а) \(\frac{41}{5}\); б) \(\frac{57}{8}\); в) 5; г) \(\frac{27}{4}\).