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2 tháng 11 2019
a, \(\frac{25^{11}.4^{33}}{8^{15}.10^{22}}=\frac{\left(5^2\right)^{11}.\left(2^2\right)^{33}}{\left(2^3\right)^{15}.\left(2.5\right)^{22}}=\frac{5^{22}.2^{66}}{2^{45}.2^{22}.5^{22}}=\frac{5^{22}.2^{66}}{2^{67}.5^{22}}=\frac{1}{2}\)
b,\(\frac{8^4.5^8.9^3}{125^3.4^7.27}=\frac{\left(2^3\right)^4.5^8.\left(3^2\right)^3}{\left(5^3\right)^3.\left(2^2\right)^7.3^3}=\frac{2^{12}.5^8.3^6}{5^9.2^{14}.3^3}=\frac{3^3}{5.2^2}=\frac{27}{20}\)
Bạn làm nốt nhé cũng tương tự thôi !!!!!!!!!
JH
30 tháng 1 2017
a)\(3^{200}\) và \(2^{300}\)
\(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)
\(2^{300}=2^{3.100}=\left(2^3\right)^{100}=8^{100}\)
Vì \(9^{100}>8^{100}=>3^{200}>8^{100}\)
b) \(125^5\) và \(25^7\)
\(125^5=\left(5^3\right)^5=5^{3.5}=5^{15}\)
\(25^7=\left(5^2\right)^7=5^{2.7}=5^{14}\)
Vì \(5^{15}>5^{14}=>125^5>25^7\)
c) \(9^{20}\) và \(27^{13}\)
\(9^{20}=\left(3^3\right)^{20}=3^{3.20}=3^{60}\)
\(27^{13}=\left(3^3\right)^{13}=3^{3.13}=3^{39}\)
Vì \(3^{60}>3^{39}=>9^{20}>27^{13}\)
d) \(3^{45}\) và \(2^{81}\)
\(3^{45}=3^{5.9}=\left(3^5\right)^9=243^9\)
\(2^{81}=2^{9.9}=\left(2^9\right)^9=512^9\)
Vì \(243^9< 512^9=>3^{45}< 2^{81}\)
K
13 tháng 8 2017
CÂU 1
\(5^{n+1}+5^n=750\)
\(=>5^n\cdot5+5^n=750\)
\(=>5^n\cdot\left(5+1\right)=750\)
\(=>5^n\cdot6=750\)
\(=>5^n=750:6\)
\(=>5^n=125\)
\(=>5^n=5^3\)
\(=>n=3\)
20 tháng 6 2017
a) $3^8:3^6=3^{8-6}=3^2$
$19^7:19^3=19^{7-3}=19^4$
$2^{10}:8^3=2^{10}:(2^3)^3=2^{10}:2^9=2^{10-9}=2^1$
$12^7:6^7=(12:6)^7=2^7$
$27^5:81^3=(3^3)^5:(3^4)^3=3^{15}:3^{12}=3^{15-12}=3^3$
b) $10^6:10=10^{6-1}=10^5$
$5^8:25^2=5^8:(5^2)^2=5^8:5^4=5^{8-4}=5^4$
$4^9:64^2=4^9:(4^3)^2=4^9:4^6=4^{9-6}=4^3$
$2^25:32^4=2^{25}:(2^5)^4=2^{25}:2^{20}=2^{25-20}=2^5$
$18^3:9^3=(18:9)^3=2^3$
20 tháng 6 2017
\(\cdot3^8:3^6=3^{8-6}=3^2\)
\(\cdot19^7:19^3=19^{7-3}=19^4\)
\(\cdot2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^9=2\)
\(\cdot12^7:6^7=\left(12:6\right)^7=2^7\)
\(\cdot27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)
\(\cdot10^6:10=10^{6-1}=10^5\)
\(\cdot5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^4=5^4\)
\(\cdot4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^6=4^3\)
\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^5\)
\(18^3:9^3=\left(18:9\right)^3=2^3\)
Giải:
\(a,27^3:3^2.\)
\(=\left(3^3\right)^3:\left(3^1\right)^2.\)
\(=3^9:3^2.\)
\(=3^{9-2}=3^7.\)
Vậy.....
\(b,\left(\dfrac{3}{5}\right)^{13}:\left(\dfrac{9}{25}\right)^5.\)
\(=\left(\dfrac{3}{5}\right)^{13}:\left[\left(\dfrac{3}{5}\right)^2\right]^5.\)
\(=\left(\dfrac{3}{5}\right)^{13}:\left(\dfrac{3}{5}\right)^{10}.\)
\(=\left(\dfrac{3}{5}\right)^{13-10}.\)
\(=\left(\dfrac{3}{5}\right)^3.\)
Vậy.....
~ Hok tốt!!! ~ =))
Bài làm
a, 273 : 32
= (33)3 : 32
= 39 : 32
= 37
Vậy ....
b, \(\left(\dfrac{3}{5}\right)^{13}:\left(\dfrac{9}{25}\right)^5\)
= \(\left(\dfrac{3}{5}\right)^{13}:\left[\left(\dfrac{3}{5}\right)^2\right]^5\)
= \(\left(\dfrac{3}{5}\right)^{13}:\left(\dfrac{3}{5}\right)^{10}\)
= \(\left(\dfrac{3}{5}\right)^3\)
Vậy ...