Rút gọn các biểu thức
b) \(\frac{36^7}{2^{15}.27^5}\)
c) \(\frac{2^7.3^6}{6^5.8^2}\)
e) \(\frac{81^5.125^{10}}{75^{15}}\)
Thanks <3
Rút gọn
c) \(\frac{2^7.3^6}{6^5.8^2}\)
\(\frac{2^7.3^6}{6^5.8^2}=\frac{2^7.3^6}{\left(2.3\right)^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{2^7.3^6}{2^{11}.3^5}=\frac{3}{2^4}=\frac{3}{16}\)
Rút gọn
b) \(\frac{36^7}{2^{15}27^5}\)
h) \(\frac{2^{18}.9^4}{6^6.8^4}\)
o) \(\frac{3^3+3.6^2+6^3}{13}\)
Thanks <3
b) \(\frac{36^7}{2^{15}.27^5}=\frac{\left(2^2.3^2\right)^7}{2^{15}.\left(3^3\right)^5}=\frac{2^{14}.3^{14}}{2^{15}.3^{15}}=\frac{1.1}{2.3}=\frac{1}{6}\)
h) \(\frac{2^{18}.9^4}{6^6.8^4}=\frac{2^{18}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^4}=\frac{2^{18}.3^8}{2^6.3^6.2^{12}}=\frac{2^{18}.3^8}{2^{18}.3^6}=\frac{1.3^2}{1.1}=9\)
o) \(\frac{3^3+3.6^2+6^3}{13}=\frac{3^3+6^2\left(3+6\right)}{13}=\frac{3^3+6^2.3^2}{13}\)
\(=\frac{3^2\left(3+6^2\right)}{13}=\frac{9.3.13}{13}=\frac{9.3.1}{1}=27\)
Tính giá trị các biểu thức sau:
a)\(\frac{8^{14}}{4^4.64^5}\) d) \(\frac{72^3.54^2}{108^4}\)
b) \(\frac{2^7.9^3}{6^5.8^2}\) e) \(\frac{9^{12}.3^5+9^{15}}{\left(2.27\right)^5.3^{14}}\)
c) \(\frac{9^{10}.27^7}{81^7.3^{15}}\)
a, 2^34/65^5
b, 3/2^4
c, 1/3^2
d,2
e, 3^6/3^5
Câu 1: Rút gọn các biểu thức sau:
C = \(\dfrac{8^2.9^5}{3^9.4^3}\)
D = \(\dfrac{81^6.9^5}{27^7.3^{11}}\)
F = \(\dfrac{8^{15}.25^7}{125^5.2^{47}}\)
G = \(\dfrac{10^2.5^3}{8.25^2}\)
\(C=\dfrac{2^6\cdot3^{10}}{3^9\cdot2^6}=3\\ D=\dfrac{3^{24}\cdot3^{10}}{3^{21}\cdot3^{11}}=\dfrac{3^{34}}{3^{32}}=3^2=9\\ F=\dfrac{2^{45}\cdot5^{14}}{5^{15}\cdot2^{47}}=\dfrac{1}{2^2\cdot5}=\dfrac{1}{20}\\ G=\dfrac{2^2\cdot5^2\cdot5^3}{2^3\cdot5^4}=\dfrac{1\cdot5}{2}=\dfrac{5}{2}\)
C=3
D=9
F=1/20
G=5/2
Em ko giải chi tiết vì nó lâu
Mong thông cảm!
C= \(\dfrac{8^2.9^5}{3^9.4^3}\)
= \(\dfrac{\left(2^3\right)^2.\left(3^2\right)^5}{3^9.\left(2^2\right)^3}\)
= \(\dfrac{2^6.3^{10}}{3^9.2^6}\)
= \(\dfrac{3^1}{1}\)
= \(\dfrac{3}{1}\)
\(\frac{9^{10}.27^7}{81^7.3^{15}}\)
\(\frac{8^3.9^5.27^5}{4^5.81^6}\)
a) \(\frac{9^{10}.27^7}{81^7.3^{15}}\)= \(\frac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}\)= \(\frac{3^{2.10}.3^{3.7}}{3^{4.7}.3^{15}}\)=\(\frac{3^{20}.3^{21}}{3^{28}.3^{15}}\)=\(\frac{3^{41}}{3^{43}}\)= \(\frac{3^{41}}{3^{41}.3^2}\)= \(\frac{1}{3^2}=\frac{1}{9}\)
b) \(\frac{8^3.9^5.27^5}{4^5.81^6}\)= \(\frac{\left(2^3\right)^3.\left(3^2\right)^5.\left(3^3\right)^5}{\left(2^2\right)^5.\left(3^4\right)^6}\)= \(\frac{2^{3.3}.3^{2.5}.3^{3.5}}{2^{2.5}.3^{4.6}}\)=\(\frac{2^9.3^{10}.3^{15}}{2^{10}.3^{24}}\)= \(\frac{2^9.3^{25}}{2^{10}.3^{24}}\)=\(\frac{2^9.3^{24}.3}{2^9.2.3^{24}}\)=\(\frac{3}{2}\)
Tính giá trị biểu thức
\(\frac{9^{10}.27^7}{81^7.3^{15}}\) \(\frac{2^{10}.3^{13}.16^3}{4^{10}.9^6}\)
Giúp em với
\(\frac{9^{10}\cdot27^7}{81^7\cdot3^{15}}=\frac{3^{20}\cdot3^{21}}{3^{28}\cdot3^{15}}=\frac{3^{41}}{3^{43}}=\frac{1}{9}\)
\(\frac{2^{10}\cdot3^{13}\cdot16^3}{4^{10}\cdot9^6}=\frac{2^{10}\cdot3^{13}\cdot2^{12}}{2^{20}\cdot3^{12}}=\frac{2^{22}\cdot3^{13}}{2^{20}\cdot3^{12}}=2^2\cdot3=12\)
rút gọn biểu thức
a) \(\frac{20^5\cdot5^{10}}{\left(4\cdot25\right)^5}\)b)\(\frac{6^3+3\cdot6^2+3^3}{-13}\)c)\(\frac{125^{12}}{5^{13}\cdot25^{11}}\)d)\(\left(2^{-1}+3^{-1}\right):\left(2^{-1}-3^{-1}\right)+\left(2^{-1}\cdot2^0\right)\cdot2^3\)
e)\(\frac{81^{11}\cdot3^{17}}{27^{10}\cdot9^{15}}\)
Rút gọn:
a,\(\frac{15.\left(1352-41\right)}{\left(1352-41\right)\left(150-15\right)}\)
b,\(\frac{2^{10}.6^{15}+3^{14}.15.4^{13}}{2^{18}.18^7.3^3+3^{15}.2^{25}}\)
rút gọn biểu thức sau
\(\frac{20.4^{15}.9^{10}-4.3^{21}.8^{10}}{10.20^{10}.6^{20}-2^{31}.27^7}\)
Phân tích ra : VD : 415=(22)15=22.15=230
Nếu làm thế này thì sẽ dể hơn vì sẽ có nhiều lũy thừa giống nhau và dễ chiệt tiêu hơn nhé bạn >