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NT
2
31 tháng 7 2016
A=\(\frac{14^{16}.21^{32}.35^{48}}{10^{16}.15^{32}.7^{96}}\)= \(\frac{\left(2.7\right)^{16}.\left(3.7\right)^{32}.\left(5.7\right)^{48}}{\left(2.5\right)^{16}.\left(3.5\right)^{32}.7^{96}}\)= \(\frac{2^{16}.7^{16}.3^{32}.7^{32}.5^{48}.7^{48}}{2^{16}.5^{16}.3^{32}.5^{32}.7^{96}}\)= \(\frac{2^{16}.7^{96}.3^{32}.5^{48}}{2^{16}.5^{48}.3^{32}.7^{96}}\)=1
QA
1
MT
21 tháng 6 2015
\(\frac{14^{16}.21^{32}.35^{48}}{10^{16}.15^{32}.7^{96}}=\frac{2^{16}.7^{16}.3^{32}.7^{32}.5^{48}.7^{48}}{2^{16}.5^{16}.3^{32}.5^{32}.7^{96}}\)
\(=\frac{2^{16}.\left(7^{16}.7^{32}.7^{48}\right).5^{48}.3^{32}}{2^{16}\left(5^{16}.5^{32}\right).3^{32}.7^{96}}=\frac{2^{16}.7^{96}.5^{48}.3^{32}}{2^{16}.5^{48}.3^{32}.7^{96}}\)=1
21 tháng 6 2019
\(\frac{14^{16}\cdot21^{31}\cdot35^{48}}{10^{16}\cdot15^{32}\cdot7^{96}}\)
\(=\frac{\left(2\cdot7\right)^{16}\cdot\left(3\cdot7\right)^{31}\cdot\left(5\cdot7\right)^{48}}{\left(2\cdot5\right)^{16}\cdot\left(3\cdot5\right)^{32}\cdot\left(7^2\right)^{48}}\)
\(=\frac{2^{16}\times3^{31}\times5^{48}\times7^{95}}{2^{16}\times3^{32}\times5^{48}\times7^{96}}\)
\(=\frac{1\times1}{3\times7}\)
\(=\frac{1}{21}\)
T
28 tháng 7 2018
\(\frac{14^{16}\times21^{32}\times35^{48}}{10^{16}\times35^{32}\times7^{96}}\)
\(=\frac{\left(2\times7\right)^{16}\times\left(3\times7\right)^{32}\times\left(5\times7\right)^{48}}{\left(2\times5\right)^{16}\times\left(5\times7\right)^{32}\times7^{96}}\)
\(=\frac{2^{16}\times7^{16}\times3^{32}\times7^{32}\times5^{48}\times7^{48}}{2^{16}\times5^{16}\times5^{32}\times7^{32}\times7^{96}}=\frac{2^{16}+7^{96}+3^{32}+5^{48}}{2^{16}\times5^{48}\times7^{32}\times7^{96}}\)
\(=\frac{3^{32}}{7^{32}}=\left(\frac{3}{7}\right)^{32}\)
21 tháng 7 2018
\(A=\frac{14^{16}-21^{32}.35^{68}}{10^{16}.15^2.7^{96}}=\frac{2^{16}.7^{16}-3^{32}.7^{32}.7^{68}.5^{68}}{5^{16}.2^{16}.3^2.5^2.7^{96}}\)
\(A=\frac{2^{16}.7^{16}-3^{32}.7^{100}.5^{68}}{5^{18}.2^{16}.3^2.7^{96}}=\frac{7^{16}.\left(2^{16}-3^{32}.7^{84}.5^{68}\right)}{5^{18}.2^{16}.3^2.7^{96}}=\frac{2^{16}-3^{32}.7^{84}.5^{68}}{5^{18}.2^{16}.3^2.7^{88}}\)
\(B=\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+2^{20}.3^{20}}{2^{20}.3^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{20}\right)}{3^{20}.\left(2^{20}-1+3^{20}\right)}\)
\(B=\frac{2^{20}}{3^{20}}\)
LK
0
HL
29 tháng 6 2017
a) \(\dfrac{15^{30}}{45^{15}}=\dfrac{15^{30}}{3^{15}.15^{15}}=\dfrac{15^{15}}{3^{15}}=5^{15}\)
b) \(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{8^5.3^8}{2^6.3^6.8^3}=\dfrac{8^2.3^2}{2^6}=\dfrac{2^6.3^2}{2^6}=3^2=9\)
c) \(\dfrac{14^{10}.21^{32}.35^{48}}{10^{10}.15^{32}.7^{96}}=\dfrac{2^{10}.7^{10}.3^{32}.7^{32}.5^{48}.7^{48}}{2^{10}.5^{10}.3^{32}.5^{32}.7^{96}}\)
= \(\dfrac{2^{10}.7^{58}.3^{32}.5^{48}}{2^{10}.5^{42}.3^{32}.7^{96}}=\dfrac{5^6}{7^{38}}\) ( Câu này làm bừa, có lẽ sai đấy :)) )
2. So sánh
a) 3200 = 9100
2300 = 8100
Vì 9100 > 8100 nên 3200 < 2300
b) 912 = 7294
268 = 6764
Vì 7294 > 6764 nên 912 > 268
c) 224 = 88
316 = 98
Vì 88 < 98 nên 224 < 316
\(=\dfrac{7^{16}\cdot2^{16}\cdot7^{32}\cdot3^{32}\cdot7^{48}\cdot5^{48}}{5^{16}\cdot2^{16}\cdot5^{32}\cdot3^{32}\cdot7^{96}}\)
\(=\dfrac{7^{96}\cdot2^{16}\cdot3^{32}\cdot5^{48}}{7^{96}\cdot2^{48}\cdot5^{48}}=\dfrac{3^{32}}{2^{32}}=1.5^{32}\)