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\(a,\left(\frac{2}{5}\right)^6.\left(\frac{25}{4}\right)^2=\left(\frac{2}{2.3}\right)^6.\left(\frac{5}{2}\right)^4\)
\(=\frac{1}{3^6}.\frac{5^4}{2^4}=\frac{5^4}{3^6.2^4}\)
\(b,\frac{100}{123}:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)\)
\(=\frac{100}{123}:\left(\frac{9+7}{12}\right)+\frac{23}{123}:\left(\frac{27-7}{15}\right)\)
\(=\frac{100}{123}:\frac{16}{12}+\frac{23}{123}:\frac{20}{15}\)
\(=\frac{100.12}{123.16}+\frac{23.15}{123.20}\)
\(=\frac{5.5.4.3.4}{41.3.4.4}+\frac{23.3.5}{41.3.4.5}\)
\(=\frac{25}{41}+\frac{23}{164}=\frac{25.4+23}{164}\)
\(=\frac{123}{164}=\frac{3}{4}\)
(-1/4+9/33-5/3)-(-5/4+6/11-48/49)
= -1/4+9/33-5/3+5/4-6/11+48/49
= -1/4+9/33+(-5/3)+5/4+(-6/11)+48/49
= 65/1617
-1/4.5/7+4/7-18/13
=-5/28+4/7-18/13
=-5/28+16/28-18/13
=11/28-18/13
=-361/364
b)4.-7/12+5.17/15
=-7/3+17/3
=10/3
c)5^4.20^4/25^5.4^5
=625.160000/9765625.1024
=1/100
\(15\times\frac{1}{4}\times\frac{-5}{7}-25\times\frac{1}{4}\times\frac{-5}{7}\)
\(=\frac{1}{4}\times\frac{-5}{7}\left(15-25\right)\)
\(=\frac{1}{4}\times\frac{-5}{7}\times\left(-10\right)\)
\(=\frac{25}{14}\)
\(15\times\frac{1}{4}\times\frac{-5}{7}-25\times\frac{1}{4}\times\frac{-5}{7}=\frac{1}{4}\times\frac{-5}{7}\left(15-25\right)=\frac{1}{4}\times\frac{-5}{7}\times\left(-10\right)=\frac{25}{14}\)