5^2x25^4/125^3=5

\(5^2\times25^{4^{125^3}}\)

Hk tốt,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k nhé Hiếu Trần

\(\frac{5^2.25^4}{125^3}=\frac{5^2.5^8}{5^9}=\frac{5^{10}}{5^9}=5\)

\(\Leftrightarrow5^3\times\left(-2\right)^3\times\left(-61\right)\times1\)\(1\)

\(=[5\times\left(-2\right)]^3\times\left(-61\right)\)

\(=\left(-10\right)^3\times\left(-61\right)\)

\(=\left(-1000\right)\times\left(-61\right)\)

\(=61000\)

1)  \(n^{20}=n\)

Vì \(0^{20}=0;1^{20}=1;\left(-1\right)^{20}=1\)

=> n = 1 hoặc n = -1 hoặc n = 0

2) \(5^{2n-1}=125\)

Ta có: \(5^3=125\Rightarrow5^{2n-1}=5^3\)

\(\Rightarrow2n-1=3\Rightarrow2n=4\Rightarrow n=2\)

Vậy n = 2

1) \(n^{20}=n\)

\(\Rightarrow n^{20}-n=0\)

\(\Rightarrow n\left(n^{19}-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}n=0\\n^{19}-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}n=0\\n^{19}=1\end{cases}}\Rightarrow\orbr{\begin{cases}n=0\\n=1\end{cases}}\)

Vậy n = 0 hoặc n = 1

2) \(5^{2n-1}=125\)

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

\(\Rightarrow2n-1=3\)

\(\Rightarrow2n=3+1\)

\(\Rightarrow2n=4\)

\(\Rightarrow n=4:2\)

\(\Rightarrow n=2\)

Vậy n = 2

_Chúc bạn học tốt_

1) \(n^{20}=n\)

\(\Rightarrow n^{20}-n=0\)

\(\Rightarrow n\left(n^{19}-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}n=0\\n^{19}-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}n=0\\n^{19}=1\end{cases}}\Rightarrow\orbr{\begin{cases}n=0\\n=1\end{cases}}\)

Vậy n = 0 hoặc n = 1

2) \(5^{2n-1}=125\)

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

\(\Rightarrow2n-1=3\)

\(\Rightarrow2n=3+1\)

\(\Rightarrow2n=4\)

\(\Rightarrow n=4:2\)

\(\Rightarrow n=2\)

Vậy n = 2

_Chúc bạn học tốt_

\(5^{x+1}=125\)

\(5^{x+1}=5^3\)

\(x+1=3\)

\(x=2\)

b, \(5^{2x-3}-2.5^2=5^2.3\)

    \(5^{2x-3}=5^2.\left(3+2\right)\)

    \(5^{2x-3}=5^3\)

    \(2x-3=3\)

     \(x=3\)

c, \(2^x=32\)

    \(2^x=2^5\)

    \(x=5\)

Chúc em học tốt.

27⁵: 81³=(3³)⁵:(3⁴)³=3¹⁵:3¹²=3³=27

125³:25⁴=(5³)³:(5²)⁴=5⁹:5⁸=5

27 ^ 5 : 81 ^ 3 = 3 ^ 15 : 3 ^ 12 = 3 ^ 3 = 27
125 ^ 3 : 25 ^ 4 = 5 ^ 9 : 5 ^ 8 = 5

\(27^5:81^3=3^{15}:3^{12}=3^3\)

\(125^3:25^4=5^9:5^8=5\)