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\(4^{18}.8^{15}=\left(2^2\right)^{18}.\left(2^3\right)^{15}\)
\(=2^{36}.2^{45}\)
\(=2^{81}\)
\(4^{15}.5^{30}=\left(2^2\right)^{15}.5^{30}\)
\(=2^{30}.5^{30}\)
\(=\left(2.5\right)^{30}\)
\(=10^{30}\)
\(\frac{3.72^2.54^2}{108^4}=\frac{3.\left(3^2.2^3\right)^2.\left(3^3.2\right)^2}{\left(3^3.2^2\right)^4}\)
\(=\frac{3.3^4.2^6.3^6.2^2}{3^{12}.2^8}\)
\(=\frac{3^{11}.2^8}{3^{12}.2^8}\)
\(=\frac{1}{3}\)
1) \(\frac{3^{10}+6^2}{5\cdot3^8+20}=\frac{3^{10}+3^2\cdot2^2}{5\cdot3^8+5\cdot2^2}=\frac{3^2\left(3^8+2^2\right)}{5\left(3^8+2^2\right)}=\frac{9}{5}\)
2) \(\frac{28^{15}\cdot3^{17}}{84^{16}}=\frac{28^{15}\cdot3^{17}}{28^{16}\cdot3^{16}}=\frac{3}{28}\)
\(5.\left\{26-\left[3.\left(5+25\right)+15\right]:15\right\}+3^4\)
\(5.\left\{26-\left[3.30+15\right]:15\right\}+81\)
\(5.\left\{26-\left[90+15\right]:15\right\}+81\)
\(5.\left\{26-105:15\right\}+81\)
\(5.\left\{26-7\right\}+81\)
\(5.19+81\)
\(176\)