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\(24^4.3^4-32^{12}:16^{12}=27^4-2^{12}=527345\)
\(a,4^x=8^4\)
\(\Rightarrow2^{2x}=2^{12}\)
\(\Rightarrow2x=12\)
\(\Rightarrow x=12:2\)
\(\Rightarrow x=6\)
\(=\dfrac{\left[\dfrac{2^{13}\cdot3^{14}}{3^{13}}+\dfrac{3^{18}}{2^{12}}:\dfrac{3^{12}}{2^{24}}\right]}{2^{12}\cdot3^4+2^{12}\cdot3^2}\)
\(=\dfrac{\left[\dfrac{2^{13}}{3}+\dfrac{2^{12}}{3^6}\right]}{2^{12}\cdot3^2\cdot\left(3^2+1\right)}=\dfrac{2^{12}\cdot\left(\dfrac{2}{3}+\dfrac{1}{3^6}\right)}{2^{12}\cdot3^2\cdot10}\)
\(=\left(\dfrac{487}{729}\right):\dfrac{1}{90}=\dfrac{4870}{81}\)
\(\frac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\)
\(=\frac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}\)
\(=\frac{15^2.16^3}{12^2.20^2.8}\)
\(=2\)
học tốt
152 . 164 - 153. 163
= 152.162.(162-15.16)
=(15.16)2.16.(16-15)
=2402.16
=57600.16
= 921600
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
24^4 . 3^4 - 32^12 : 16^12
= (24 . 4)^4 - (32 : 16)^12
= 96^4 - 2^12
244.34-3212:1612=26869760