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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) 3.243.26 = 46656
b) 810 : 167 = \(\frac{8^{10}}{16^7}=4\)
\(\frac{8^{11}.3^{17}}{27^{10}.9^{15}}=\frac{8^{11}.3^{17}}{3^{30}.3^{30}}=\frac{8^{11}}{3^{13}.3^{30}}=\frac{8^{11}}{3^{43}}\)
\(\frac{\left(5^4-5^3\right)^3}{125^4}=\frac{[\left(5-1\right).5^3]^3}{5^{12}}=\frac{\left(4.5^3\right)^3}{5^{12}}=\frac{64.5^9}{5^{12}}=\frac{64}{5^3}=\left(\frac{4}{5}\right)^3\)
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+6^{20}}{6^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{30}\right)}{3^{20}.\left(2^{20}-2+3^{20}\right)}=\frac{2^{20}}{3^{20}}=\left(\frac{2}{3}\right)^{20}\)
a) \(8^{15}.4^{13}=\left(2^3\right)^{15}.\left(2^2\right)^{13}=2^{45}.2^{26}=2^{71}\)
b) \(\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{4}\right)^{28}=\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{2^2}\right)^{28}=\frac{1}{2^{18}}.\frac{1}{2^{56}}=\frac{1}{2^{74}}=\left(\frac{1}{2}\right)^{74}\)
c) \(9^{12}.27^{10}=\left(3^2\right)^{12}.\left(3^3\right)^{10}=3^{24}.3^{30}=3^{54}\)
a) = (23)15. (22)13 = 245.226 = 271
b) = \(\left(\frac{1}{2}\right)^{18}.\left(\left(\frac{1}{2}\right)^2\right)^{28}=\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{2}\right)^{56}=\left(\frac{1}{2}\right)^{18+56}=\left(\frac{1}{2}\right)^{74}\)
c) = (32)12.(33)10 = 324.330 = 324+30 = 354
Số hữu tỉ \(\frac{8}{625}\) được viết dưới dạng lũy thừa là :
\(\frac{8}{625}=\frac{2^3}{5^4}\)
\(\frac{8}{625}=\frac{2^3}{25^2}\)
\(\frac{8}{625}=\frac{2^3}{25^2}\)
\(\frac{8}{625}=\frac{2^3}{5^4}\)
108 : 28 = (10:2)8 = 58