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T
10 tháng 9 2023
\(a,\dfrac{5^{16}\cdot27^7}{125^5\cdot9^{11}}=\dfrac{5^{16}\cdot\left(3^3\right)^7}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}\)
\(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)
\(b,\left(-0,2\right)^2\cdot5-\dfrac{2^{13}\cdot27^3}{4^6\cdot9^5}\)
\(=0,04\cdot5-\dfrac{2^{13}\cdot\left(3^3\right)^3}{\left(2^2\right)^6\cdot\left(3^2\right)^5}\)
\(=0,2-\dfrac{2^{13}\cdot3^9}{2^{12}\cdot3^{10}}\)
\(=0,2-\dfrac{2}{3}\)
\(=-\dfrac{7}{15}\)
\(c,\dfrac{5^6+2^2\cdot25^3+2^3\cdot125^2}{26\cdot5^6}\)
\(=\dfrac{5^6+2^2\cdot\left(5^2\right)^3+2^3\cdot\left(5^3\right)^2}{5^6\cdot26}\)
\(=\dfrac{5^6+4\cdot5^6+8\cdot5^6}{5^6\cdot26}\)
\(=\dfrac{5^6\left(1+4+8\right)}{5^6\cdot26}\)
\(=\dfrac{13}{26}\)
\(=\dfrac{1}{2}\)
#\(Toru\)
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
10 tháng 9 2023
\(a,\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{\left(5^2\right)^8.9^7.3^7}{25^5.5^5.9^{11}}\\ =\dfrac{25^8.9^7.\left(3^2\right)^3.3}{25^5.\left(5^2\right)^2.5.9^{11}}=\dfrac{25^8.9^7.9^3.3}{25^5.25^2.5.9^{11}}\\ =\dfrac{25^8.9^{10}.3}{25^7.5.9^{11}}=\dfrac{25^7.9^{10}.25.3}{25^7.9^{10}.5.9}\\ =\dfrac{25.3}{5.9}=\dfrac{5.5.3}{5.3.3}=\dfrac{5}{3}\)
12 tháng 7 2018
2, 100^2+200^2+300^2+..+1000^2
=100^2+2^2×100^2+3^2×100^2+...+100^2×10^2
=100^2×( 1^2+2^2+3^2+..+10^2)
=100^2×385
= 3850000
15 tháng 8 2023
`@` `\text {Ans}`
`\downarrow`
`a,`
`5.125.25 \div 5^6`
`=`\(5\cdot5^3\cdot5^2\div5^6\)
`=`\(5^{1+3+2-6}=5^{6-6}=5^0=1\)
`b,`
\(2^{14}\div\left(2^6\cdot32\right)\)
`=`\(2^{14}\div\left(2^6\cdot2^5\right)\)
`=`\(2^{14}\div2^{11}=2^3\)
`c,`
`3.3^5\div 27`
`=`\(3\cdot3^5\div3^3\)
`=`\(3^{1+5-3}\)
`=`\(3^3\)
`d,`
\(2^{15}\div\left(2^6\cdot32\right)=2^{15}\div\left(2^6\cdot2^5\right)=2^{15}\div2^{11}=2^4\)
`e,`
\(3^2\cdot27\div81=3^2\cdot3^3\div3^4=3\)
`g,`
\(100\cdot1000\cdot10000-10^9=10^2\cdot10^3\cdot10^4-10^9\)
`=`\(10^9-10^9=0\)
`h,`
\(125^4\div5^9=\left(5^3\right)^4\div5^9=5^{12}\div5^9=5^3\)
HN
10 tháng 7 2017
1. Tìm n, biết:
a) \(\dfrac{-32}{\left(-2\right)^n}=4\)
\(\Rightarrow\dfrac{\left(-2\right)^5}{\left(-2\right)^n}=\left(-2\right)^2\)
\(\Rightarrow\left(-2\right)^n.\left(-2\right)^2=\left(-2\right)^5\)
(-2)n + 2 = (-2)5
n + 2 = 5
n = 5 - 2
n = 3.
b) \(\dfrac{8}{2^n}=2\)
\(\Rightarrow\dfrac{2^3}{2^n}=2\)
\(\Rightarrow\) 2n . 2 = 23
n + 1 = 3
n = 3 - 1
n = 2.
c) \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{2n-1}=\left(\dfrac{1}{2}\right)^3\)
2n - 1 = 3
2n = 3 + 1
2n = 4
n = 4 : 2
n = 2.
2. Tính:
a) \(\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{4}\right)^2\)
\(=\left(\dfrac{1}{2}\right)^3.\left[\left(\dfrac{1}{2}\right)^2\right]^2\)
\(=\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{2}\right)^4\)
\(=\left(\dfrac{1}{2}\right)^7\)
\(=\dfrac{1}{128}\)
b) 273 : 93
= (33)3 : (32)3
= 39 : 36
= 33
= 27
c) 1252 : 253
= (53)2 : (52)3
= 56 : 56
= 1
d) \(\dfrac{27^2.8^5}{6^6.32^3}\)
\(=\dfrac{\left(3^3\right)^2.\left(2^3\right)^5}{6^6.\left(2^5\right)^3}\)
\(=\dfrac{3^6.2^{15}}{6^6.2^{15}}\)
\(=\dfrac{3^6}{6^6}\)
\(=\dfrac{1}{64}.\)
10 tháng 7 2017
B2 :
b) 27\(^3\): 9\(^3\)= (27:9)\(^3\)= 3\(^3\)
c) 125\(^2\): 25\(^3\)= 15625 : 15625 = 1
HP
1
VM
8 tháng 9 2019
a) \(5^n.25=125^2\)
\(\Rightarrow5^n.5^2=\left(5^3\right)^2\)
\(\Rightarrow5^n.5^2=5^6\)
\(\Rightarrow5^n=5^6:5^2\)
\(\Rightarrow5^n=5^4\)
\(\Rightarrow n=4\)
Vậy \(n=4.\)
b) \(3^n.9^2=27^3\)
\(\Rightarrow3^n.\left(3^2\right)^2=\left(3^3\right)^3\)
\(\Rightarrow3^n.3^4=3^9\)
\(\Rightarrow3^n=3^9:3^4\)
\(\Rightarrow3^n=3^5\)
\(\Rightarrow n=5\)
Vậy \(n=5.\)
c) \(2^4.4^n=8^6\)
\(\Rightarrow\left(2^2\right)^2.4^n=2^{18}\)
\(\Rightarrow4^2.4^n=\left(2^2\right)^9\)
\(\Rightarrow4^2.4^n=4^9\)
\(\Rightarrow4^n=4^9:4^2\)
\(\Rightarrow4^n=4^7\)
\(\Rightarrow n=7\)
Vậy \(n=7.\)
Chúc bạn học tốt!
a) \(\left(\frac{1}{2}\right)^3.\left(\frac{1}{4}\right)^2\)
\(=\frac{1}{8}.\frac{1}{8}\)
\(=\frac{1}{16}\)
b) \(27^3:9^3\)
\(=\left(27:9\right)^3\)
\(=3^3\)
\(=27\)
c) \(125^2:25^3\)
\(=\left(5^3\right)^2:\left(5^2\right)^3\)
\(=5^6:5^6\)
\(=\left(5:5\right)^6\)
\(=1^6\)
\(=1\)
d) \(\frac{27^2.8^5}{6^6.32^3}\)
Phân tích hợp số ra thừa số nguyên tố:
27 = 33, 8 = 23, 6 = 2.3, 32= 25
\(\Rightarrow\frac{\left(3^3\right)^2.\left(2^3\right)^5}{\left(2.3\right)^6.\left(2^5\right)^3}\)
\(\Rightarrow\frac{3^6.2^{15}}{\left(2.3\right)^6.2^{15}}\)
\(\Rightarrow\frac{3^6}{2^6.3^6}\)
\(\Rightarrow\frac{1}{2^6}=\frac{1}{64}\)
a) 1/8.1/16=1/128
b) 3^9: 3^6=3^3=27
c) 5^6: 5^6=1
d) 3^6.2^15/ 2^6.3^6.2^15=1/2^6=1/64