\(⋮\)225

 b) 125

K
Khách

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a) 8110 - 2713 - 921 \(⋮\)225

= 8110 - 273 - 921 : 225

= ( 34 )10 - ( 33 )3 - ( 32 )21

= 340 - 39 - 342

= 339 . ( -25 )

= -225 . 337

-225 nhân 1 số tự nhiên thì luôn luôn chia hết cho 225

5 tháng 7 2017

1) Tính

a) 253 : 52 = (52)3 : 52 = 56 : 52 = 54 = 625

\(b)\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^6=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^6=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^{12}=\left(\dfrac{3}{7}\right)^9\) d) 9 . 32 . \(\dfrac{1}{81}\) . 32 = 32 . 32 . \(\dfrac{1}{3^4}\) . 32 = 9

2) Tìm x thuộc Q, biết:

a) 3x + 2 = 27

=> 3x + 2 = 33

x + 2 = 3

x = 3 - 2

x = 1

b) \(\left(\dfrac{1}{2}x-3\right)^4=81\)

\(\Rightarrow\left(\dfrac{1}{2}x-3\right)^4=3^4\)

\(\dfrac{1}{2}x-3=3^{ }\)

\(\dfrac{1}{2}x=3+3\)

\(\dfrac{1}{2}x=9\)

\(x=9:\dfrac{1}{2}\)

\(x=18\)

c) \(\left(x-\dfrac{1}{2}\right)^3=-27\)

\(\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\left(-3\right)^3\)

\(x-\dfrac{1}{2}=-3\)

\(x=-3+\dfrac{1}{2}\)

\(x=\dfrac{-5}{2}\)

d) 5 . 5x + 1 = 125

5x + 1 = 125 : 5

5x + 1 = 25

5x + 1 = 52

x + 1 = 2

x = 2 - 1

x = 1.

28 tháng 9 2017

a, \(10^9+10^8+10^7⋮222\)

Ta có:\(10^9+10^8+10^7=10^7.\left(10^2+10+1\right)\)

\(=10^7.111=5^7.2^7.111=5^7.2^6.2.111=5^7.2^6.222\)

Vì 222\(⋮222\Rightarrow5^7.2^6.222⋮222\)

Vậy \(10^9+10^8+10^7⋮222\)

b) 817 - 279 - 913 45

\(\)Ta có: \(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=3^{28}-3^{27}-3^{26}=3^{26}.\left(3^2-3-1\right)\)

\(=3^{26}.5=3^{24}.3^2.5=3^{24}.45\)

\(45⋮45\Rightarrow3^{24}.45⋮45\)

Vậy \(81^7-27^9-9^{13}⋮45\)

CHÚC BẠN HỌC TỐT!!

28 tháng 9 2017

a) \(10^9+10^8+10^7\)

\(=10^7\left(10^2+10+1\right)\)

\(=5^7.2^7.\left(100+10+1\right)\)

\(=5^7.2^6.2\left(100+10+1\right)\)

\(=5^7.2^6.2.111\)

\(=5^7.2^6.222⋮222\)

21 tháng 10 2019

a) Câu này thiếu đề nhé bạn.

b) \(\frac{25}{5^n}=5\)

\(\Rightarrow5^n=25:5\)

\(\Rightarrow5^n=5\)

\(\Rightarrow5^n=5^1\)

\(\Rightarrow n=1\)

Vậy \(n=1.\)

c) \(\frac{81}{\left(-3\right)^n}=-243\)

\(\Rightarrow\left(-3\right)^n=81:\left(-243\right)\)

\(\Rightarrow\left(-3\right)^n=-\frac{1}{3}\)

\(\Rightarrow\left(-3\right)^n=\left(-3\right)^{-1}\)

\(\Rightarrow n=-1\)

Vậy \(n=-1.\)

e) \(\left(\frac{1}{3}\right)^n=\frac{1}{81}\)

\(\Rightarrow\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^4\)

\(\Rightarrow n=4\)

Vậy \(n=4.\)

f) \(\left(-\frac{3}{4}\right)^n=\frac{81}{256}\)

\(\Rightarrow\left(-\frac{3}{4}\right)^n=\left(-\frac{3}{4}\right)^4\)

\(\Rightarrow n=4\)

Vậy \(n=4.\)

Chúc bạn học tốt!

22 tháng 10 2019

d) \(\frac{1}{2}.2^n+4.2^n=9.2^5\)

\(\Rightarrow2^n.\left(\frac{1}{2}+4\right)=288\)

\(\Rightarrow2^n.\frac{9}{2}=288\)

\(\Rightarrow2^n=288:\frac{9}{2}\)

\(\Rightarrow2^n=64\)

\(\Rightarrow2^n=2^6\)

\(\Rightarrow n=6\)

Vậy \(n=6.\)

g) \(-\frac{512}{343}=\left(-\frac{8}{7}\right)^n\)

\(\Rightarrow\left(-\frac{8}{7}\right)^n=\left(-\frac{8}{7}\right)^3\)

\(\Rightarrow n=3\)

Vậy \(n=3.\)

h) \(5^{-1}.25^n=125\)

\(\Rightarrow5^{-1}.5^{2n}=5^3\)

\(\Rightarrow5^{-1+2n}=5^3\)

\(\Rightarrow-1+2n=3\)

\(\Rightarrow2n=3+1\)

\(\Rightarrow2n=4\)

\(\Rightarrow n=4:2\)

\(\Rightarrow n=2\)

Vậy \(n=2.\)

k) \(3^{-1}.3^n+6.3^{n-1}=7.3^6\)

\(\Rightarrow3^{n-1}+6.3^{n-1}=7.3^6\)

\(\Rightarrow3^{n-1}.\left(1+6\right)=7.3^6\)

\(\Rightarrow3^{n-1}.7=7.3^6\)

\(\Rightarrow n-1=6\)

\(\Rightarrow n=6+1\)

\(\Rightarrow n=7\)

Vậy \(n=7.\)

Chúc bạn học tốt!

20 tháng 9 2017

bn ơi con b) có vấn đề

15 tháng 8 2017

a, \(81^7-27^9-9^{13}\)

\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=3^{28}-3^{27}-3^{26}\)

\(=3^{26}\left(3^2-3-1\right)\)

\(=3^{25}.3.5\)

\(=3^{25}.15⋮15\)

\(\Leftrightarrow81^7-27^9-9^{13}⋮15\Leftrightarrowđpcm\)

15 tháng 8 2017

a. Ta có: \(81^7-27^9-9^{13}\)

\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}\)

\(=3^{25}\left(3^3-3^2-3\right)=3^{25}\left(27-9-3\right)=3^{25}\cdot15\)

\(15⋮15\) nên \(3^{25}\cdot15⋮15\)

\(\Rightarrow81^7-27^9-9^{13}⋮15\) (đpcm)

b. Ta có: \(24^{54}\cdot54^{24}\cdot2^{10}\)

\(=\left(2^3\cdot3\right)^{54}\cdot\left(3^3\cdot2\right)^{24}\cdot2^{10}\)

\(=\left(2^3\right)^{54}\cdot3^{54}\cdot\left(3^3\right)^{54}\cdot2^{54}\cdot2^{10}\)

\(=2^{162}\cdot2^{24}\cdot2^{10}\cdot3^{54}\cdot3^{72}=2^{196}\cdot3^{126}\)

\(72^{63}=\left(2^3\cdot3^2\right)^{63}\)

\(=\left(2^3\right)^{63}\cdot\left(3^2\right)^{63}=2^{189}\cdot3^{126}\)

\((2^{196}\cdot3^{126})⋮\left(2^{189}\cdot3^{126}\right)\)

\(\Rightarrow24^{54}\cdot54^{24}\cdot2^{10}⋮72^{63}\) (đpcm)

3 tháng 8 2018

\(1.a)\) Ta có: \(\left\{{}\begin{matrix}64^8=\left(8^2\right)^8=8^{16}\\16^{12}=8^{12}.2^{12}=8^{12}.\left(2^3\right)^4=8^{12}.8^4=8^{16}\end{matrix}\right.\)

Có: \(8^{16}=8^{16}\Rightarrow64^8=16^{12}\)

Vậy...

\(b)\) Ta có: \(\left\{{}\begin{matrix}\left(-5\right)^{30}=\left[\left(-5\right)^3\right]^{10}=\left(-125\right)^{10}\\\left(-3\right)^{50}=\left[\left(-3\right)^5\right]^{10}=\left(-243\right)^{10}\end{matrix}\right.\)

Có: \(\left(-125\right)^{10}< \left(-243\right)^{10}\Rightarrow\left(-5\right)^{30}< \left(-3\right)^{50}\)

Vậy...

\(c)\) Ta có: \(\left\{{}\begin{matrix}2^{27}=\left(2^3\right)^9=8^9\\3^{18}=\left(3^2\right)^9=9^9\end{matrix}\right.\)

Có: \(8^9< 9^9\Rightarrow2^{27}< 3^{18}\)

Vậy...

\(d)\) Ta có: \(\left\{{}\begin{matrix}\left(\dfrac{1}{25}\right)^{10}=\left[\left(\dfrac{1}{5}\right)^2\right]^{10}=\left(\dfrac{1}{5}\right)^{20}\\\left(\dfrac{1}{125}\right)^8=\left[\left(\dfrac{1}{5}\right)^3\right]^8=\left(\dfrac{1}{5}\right)^{24}\end{matrix}\right.\)

Có: \(\left(\dfrac{1}{5}\right)^{20}< \left(\dfrac{1}{5}\right)^{24}\Rightarrow\left(\dfrac{1}{24}\right)^{10}< \left(\dfrac{1}{125}\right)^8\)

Vậy...

\(e)\)Có: \(32^9=\left(2^5\right)^9=2^{45}< 2^{52}=\left(2^4\right)^{13}=16^{13}< 18^{13}\)

\(\Rightarrow32^9< 18^{13}\)

Vậy...

2 tháng 8 2018

a) \(25^3:5=5^{6-1}=5^4=625\)

Học tốt~