(-3)ⁿ/81=-27

(-3)ⁿ/(-3)⁴=(-3)³

=>n-4=3

n=3+4

n=7

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(5.2^2\right)^4}{\left(5^2\right)^5.\left(2^2\right)^5}=\frac{5^4.5^4.2^8}{5^{10}.2^{10}}=\frac{5^8.2^8}{5^{10}.2^{10}}=\frac{1}{5^2.2^2}=\frac{1}{25.4}=\frac{1}{100}\)

 ta có \(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)

\(a^3+b^3=\left(a^3+3a^2b+3ab^2+b^3\right)-3a^2b-3ab^2=\left(a+b\right)^3-3ab\left(a+b\right)\)

đề sai nha

a) với x>=5 => E=3x+1+x-5=4x-4=4(x-1)

b) th1: x<-1 => E=-x-1-x+3=-2x+2=-2(x-1)

th2: \(-1\le x\le3\)=> E=x+1-x+3=4

th3: x>3 =>E= x+1+x-3=2x-2=2(x-1)

\(\frac{x}{5}=\frac{y}{7}\Rightarrow\frac{x}{5}=\frac{2y}{14}\)và x+2y=38

Áp dụng t/c của dãy tỉ só bằng nhau ta có:

\(\frac{x}{5}=\frac{2y}{14}=\frac{x+2y}{5+14}=\frac{38}{19}=2\)

=>x=2.5=10

y=2.7=14

x=10

    y=14

ta có: |a-b|=|b-a|

=> \(\left|x^2+x+3\right|+\left|x^2+x-6\right|=\left|x^2+x+3\right|+\left|6-x^2-x\right|\)

áp dụng bđt: |a|+|b|>= |a+b| ta có: \(\left|x^2+x+3\right|+\left|6-x^2-x\right|\ge\left|x^2+x+3+6-x^2-x\right|=\left|9\right|=9\Rightarrow Min=9\Leftrightarrow x=0\)

c. \(3^{-1}\cdot3^x+5\cdot3^{x-1}=162\)

\(\Leftrightarrow3^{x-1}\left(1+5\right)=162\)

\(\Leftrightarrow3^{x-1}=27\)

\(\Leftrightarrow3^{x-1}=3^3\)

\(\Leftrightarrow x-1=3\)

\(\Leftrightarrow x=4\)

a)16/2ⁿ=2

=>16=2ⁿ.2

=>8=2ⁿ

=>2³=2ⁿ

=>n=3

b)(-3)ⁿ/81=-27

<=>(-3)ⁿ=(-27).81

<=>(-3)ⁿ=-2187

<=>(-3)ⁿ=(-3)⁷

<=>n=7

c)8ⁿ:2ⁿ=4

<=>8ⁿ=4.2ⁿ

<=>2³ⁿ=2²⁺ⁿ

<=>3n=2+n

<=>2n=2

<=>n=1