a) \(4^{10}.2^{30}=\left(2^2\right)^{10}.2^{30}=2^{2.10}.2^{30}=2^{20}.2^{30}=2^{20+30}=2^{50}\)
b) \(9^{25}.27^4.81^3=\left(3^2\right)^{25}.\left(3^3\right)^4.\left(3^4\right)^3=3^{3.25}.3^{3.4}.3^{4.3}=3^{75}.3^{12}.3^{12}=3^{75+12+12}=3^{99}\)
c) \(25^{50}.125^5=\left(5^2\right)^{50}.\left(5^3\right)^5=5^{2.50}.5^{3.5}=5^{100}.5^{15}=5^{100+15}=5^{115}\)
d) \(64^3.4^8.16^4=\left(4^3\right)^3.4^8.\left(4^2\right)^4=4^{3.3}.4^8.4^{2.4}=4^9.4^8.4^8=4^{9+8+8}=4^{25}\)
e) \(3^8:3^6=3^{8-6}=3^2\)
f) \(2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^{3.3}=2^{10}:2^9=2^{10-9}=2\)
g) \(12^7:6^7=\left(12:6\right)^7=2^7\)
h_ \(21^5:81^3\)kết quả là số dư nên không tính ( đề sai )
i) \(5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^{2.2}=5^8:5^4=5^{8-4}=5^4\)
k) \(4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^{3.2}=4^9:4^6=4^{9-6}=4^3\)
l) \(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{5.4}=2^{25}:2^{20}=2^{25-20}=2^5\)
m) \(125^3:25^4=\left(5^3\right)^3:\left(5^2\right)^4=5^{3.3}:5^{2.4}=5^9:5^8=5\)
h).215 /813=75.35/312=75.1/37
