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31 tháng 7 2018
a) \(\frac{15^5.10^5}{6^6.25^6}\)= (15.10)^5/(6.25)^6=150^5/150^6=1/150
11 tháng 7 2019
\(^{\frac{\left(5^4-5^3\right)^3}{125^4}=\frac{\left[5^3\cdot\left(5-1\right)\right]^3}{\left(5^3\right)^4}=\frac{\left[5^3\cdot4\right]^3}{5^3\cdot4}=\frac{\left(5^3\right)^3\cdot4^3}{5^{12}}=\frac{5^9\cdot4^3}{5^9\cdot5^3}=\frac{4^3}{5^3}}\)
S
2
A
21 tháng 6 2018
\(\frac{15^5.10^5}{6^6.25^6}\)
\(=\frac{3^5.5^5.2^5.5^5}{3^6.2^6.5^{12}}\)
\(=\frac{3^5.2^5.5^{10}}{3^6.2^6.5^{12}}\)
\(=\frac{1}{3.2.5^2}\)
\(\frac{\left(5^4.5^3\right)^3}{125^4}\)
\(=\frac{\left(5^7\right)^3}{5^{12}}\)
\(=\frac{5^{21}}{5^{12}}\)
\(=5^9\)
LM
20 tháng 8 2016
a)\(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}=\frac{3^6.\left(3^2.5\right)^4-\left(3.5\right)^{13}.5^{-9}}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}=\frac{3^6.3^8.5^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)
\(=\frac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{13}.5^4.\left(3-1\right)}{3^{12}.5^6\left(1+1\right)}=\frac{3^{13}.5^4}{3^{12}.5^6}=\frac{3}{5^2}=\frac{3}{25}\)
b)\(\frac{4^6.9^5+6^9.120}{-8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5}{-\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{-2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-\left(2^{12}.3^{12}+2^{11}.3^{11}\right)}=\frac{2^{12}.3^{10}\left(1+5\right)}{-\left[2^{11}.3^{11}\left(2.3+1\right)\right]}=\frac{2.6}{-\left(3.7\right)}=\frac{4}{-7}\)
T
4 tháng 10 2023
\(a,\dfrac{15^3}{5^4}\)
\(=\dfrac{\left(3\cdot5\right)^3}{5^4}\)
\(=\dfrac{3^3\cdot5^3}{5^4}\)
\(=\dfrac{3^3}{5}\)
\(=\dfrac{27}{5}\)
\(---\)
\(b,\dfrac{21^3}{7^4}\)
\(=\dfrac{\left(3\cdot7\right)^3}{7^4}\)
\(=\dfrac{3^3\cdot7^3}{7^4}\)
\(=\dfrac{3^3}{7}\)
\(=\dfrac{27}{7}\)
\(---\)
\(c,\dfrac{6^6}{3^8}\)
\(=\dfrac{\left(2\cdot3\right)^6}{3^8}\)
\(=\dfrac{2^6\cdot3^6}{3^8}\)
\(=\dfrac{2^6}{3^2}\)
\(=\dfrac{64}{9}\)
#\(Toru\)
PH
4
HT
23 tháng 11 2017
Phạm Hồng Anh k tớ nhé
a) \(\frac{6^{15}+6^{13}}{6^{12}}=\frac{6^{13}.\left(6^2+1\right)}{6^{12}}=6.37=222\)
b) \(\frac{2^6.5^7}{10^6}=\frac{2^6.5^6.5}{10^6}=\frac{10^6.5}{10^6}=5\)
BM
23 tháng 11 2017
a, Ta có: \(A=\frac{6^{15}+6^{13}}{6^{12}}=\frac{6^{12}\left(6^3+6\right)}{6^{12}}=6^3+6\) \(=222\)
b, Ta có: \(B=\frac{2^6.5^7}{10^6}=\frac{2^6.5^6.5}{10^6}=\frac{\left(2.5\right)^6.5}{10^6}\) \(=\frac{10^6.5}{10^6}=5\)
4 tháng 1 2019
Biến đổi :
\(\frac{125\cdot8^2}{30^6\cdot\left(-15\right)^2}=\frac{5^3\cdot\left(2^3\right)^2}{2^6\cdot3^6\cdot5^6\cdot3^2\cdot5^2}\)
\(=\frac{5^3\cdot2^6}{2^6\cdot3^8\cdot5^8}=\frac{1}{3^8\cdot5^5}\)
\(\Rightarrow\left(\frac{-2}{5}\right)^5:\left(\frac{125\cdot8^2}{30^6\cdot\left(-15\right)^2}\right)^2\)
\(=\frac{\left(-2\right)^5}{5^5}:\frac{1^2}{\left(3^8\cdot5^5\right)^2}\)
\(=\frac{\left(-2\right)^5\cdot3^{16}\cdot5^{10}}{5^5}\)
\(=\left(-2\right)^5\cdot3^{16}\cdot5^5\)
22 tháng 1 2019
\(A=\frac{2^{19}.\left(2^3\right)^3+15.\left(2^2\right)^9.\left(3^2\right)^4}{2^9.3^9.2^{10}+\left(2^2.3\right)^{10}}=\frac{2^{19}.3^9+15.2^{18}.3^8}{2^{19}.3^9+2^{20}.3^{10}}=\frac{2^{18}.3^8.\left(2.3+15\right)}{2^{19}.3^9.\left(1+2.3\right)}\)
\(=\frac{2^{18}.3^8.21}{2^{19}.3^9.7}=\frac{21}{2.3.7}=\frac{1}{2}\)
\(\dfrac{6^6\cdot25^6}{15^5\cdot10^5}=\dfrac{\left(6\cdot25\right)^6}{\left(15\cdot10\right)^5}=\dfrac{150^6}{150^5}=150\)