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Ta có: \(\frac{4^2.25^2+32.5^3}{2^3.5^2}=\frac{2^4.5^4+2^5.5^3}{2^3.5^2}\)
\(=\frac{2^4.5^3.\left(5+2\right)}{2^3.5^2}\)
\(=2.5.7\)
\(=70\)
(103 + 104 + 1252) : 53
= (23.53 + 24.54 + 56) : 53
= 53.(23 + 24.5 + 53) : 53
= 23 + 24.5 + 53
= 8 + 16.5 + 125
= 8 + 80 + 125
= 213
\(\frac{69}{157}-\left\{2+\left[3+\left(4+5^{-1}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left\{2+\left[3+\left(4+\frac{1}{5}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left\{2+\left[3+\left(\frac{21}{5}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left[2+\left(3+\frac{5}{21}\right)^{-1}\right]^{-1}\)
\(=\frac{69}{157}-\left[2+\left(\frac{68}{21}\right)^{-1}\right]^{-1}\)
\(=\frac{69}{157}-\left(2+\frac{21}{68}\right)^{-1}\)
\(=\frac{69}{157}-\left(\frac{157}{68}\right)^{-1}\)
\(=\frac{69}{157}-\frac{68}{157}\)
\(=\frac{1}{157}\)
\(\frac{3^2.3^5}{3^4}=3^3=27\)
27