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a/108.28=(10.2)8=208
b/108:28=(10:2)8=58
c/254.28=(52)4.28=58.28=(5.2)8=108
d/158.94=158.(32)4=158.38=(15.3)8=458
e/272:253=(33)2:(52)3=36:56=(3:5)6=(3/5)6
a)
\(25^4.2^8=25^4.4^4=100^4\)
b)
\(15^8.9^4=\left(15^2\right)^4.9^4=225^4.9^4=\left(225.9\right)^4=2025^4\)
c)
\(27^2:25^3=\frac{729}{15625}=\left(\frac{27}{125}\right)^2\)
\(\frac{8^{11}.3^{17}}{27^{10}.9^{15}}=\frac{8^{11}.3^{17}}{3^{30}.3^{30}}=\frac{8^{11}}{3^{13}.3^{30}}=\frac{8^{11}}{3^{43}}\)
\(\frac{\left(5^4-5^3\right)^3}{125^4}=\frac{[\left(5-1\right).5^3]^3}{5^{12}}=\frac{\left(4.5^3\right)^3}{5^{12}}=\frac{64.5^9}{5^{12}}=\frac{64}{5^3}=\left(\frac{4}{5}\right)^3\)
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+6^{20}}{6^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{30}\right)}{3^{20}.\left(2^{20}-2+3^{20}\right)}=\frac{2^{20}}{3^{20}}=\left(\frac{2}{3}\right)^{20}\)
\(10^8.2^8=\left(2.10\right)^8=20^8\)
\(10^8:2^8=\left(10:2\right)^8=5^8\)
\(25^4.2^8=5^8.2^8=\left(2.5\right)^8=10^8\)
\(15^8.9^4=15^8.3^8=\left(15.3\right)^8=45^8\)
\(27^2:25^3=3^6:5^6=\left(\frac{3}{5}\right)^6\)
a)
\(10^8.2^8=\left(10.2\right)^8=20^8\)
b)
\(10^8:2^8=\left(10:2\right)^8=5^8\)
c)
\(25^4.2^8=\left(5^2\right)^4.2^8=5^8.2^8=\left(2.5\right)^8=10^8\)
d)
\(15^8.9^4=15^8.\left(3^2\right)^4=15^4.3^4=45^4\)
e)
\(27^2:25^3=\left(3^3\right)^2:\left(5^2\right)^3=3^6:5^6=\left(\frac{3}{5}\right)^6\)
a.108.28=(10.2)8=> 208
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