tính giá trị biểu thức M

P=(7-4)^(7-5)=9

a)

\(2\left|x-6\right|+7x-2=\left|x-6\right|+7x\)

\(\Rightarrow2\left|x-6\right|-2-\left|x-6\right|=0\)

\(\Rightarrow\left|x-6\right|=2\)

\(\Rightarrow\left[{}\begin{matrix}x-6=2\\x-6=-2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=4\end{matrix}\right.\)

b)

\(....\Leftrightarrow4\left(x-5\right)+7\left(x-5\right)-10\left(x-5\right)=-3\)

\(\Rightarrow x-5=-3\)

\(\Rightarrow x=2\)

\(A=\frac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}\)

\(=\frac{2^3\left(2^{27}.5^7+2^{10}.5^{27}\right)}{2^{27}.5^7+2^{10}.5^{27}}\)

\(=2^3=8\)

\(\frac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}+\frac{2^{13}.5^7\left(2^{17}+5^{20}\right)}{2^{10}.5^7\left(2^{17}+5^{20}\right)}=2^3=8\)

\(P=\left(x-4\right)^{\left(x-5\right)^{\left(x-6\right)^{\left(x+6\right)^{\left(x+5\right)}}}}=\left(7-4\right)^{\left(7-5\right)^{\left(7-6\right)^{\left(7+6\right)^{\left(7+5\right)}}}}=3^{2^{1^{13^{12}}}}\)

\(=3^{2^1}=3^2=9\)

Thay x = 7 vào biểu thức ta có:

\(\left(x-4\right)^{\left(x-5\right)^{\left(x-6\right)^{\left(x+6\right)^{\left(x+5\right)}}}}=\left(7-4\right)^{\left(7-5\right)^{\left(7-6\right)^{\left(7+6\right)^{\left(7+5\right)}}}}\)

\(=3^{2^{1^{13^{12}}}}\) . Vì 1 là số có mũ lên bao nhiêu cũng có kết quả là 1 nên:

\(3^{2^{1^{13^{12}}}}=3^2=9\)

Vậy P = 9

Chúc học tốt!

Thay x=7 vào P ta có:

\(\left(7-4\right)^{\left(7-5\right)^{\left(7-6\right)^{\left(7+6\right)^{\left(7+5\right)}}}}\)

\(=3^{2^{1^{13^{12}}}}=3^{2^1}\)(do \(1^n=1\)với \(n\in N\)*)

\(=3^2=9\)

Chúc bạn học tốt!!!

a) \(\left(x-1\right)^3=8=2^3\)

\(x-1=2\)

\(x=2+1=3\)

b) \(7^{2x-6}=49=7^2\)

\(2x-6=2\)

\(2x=6+2=8\)

\(x=8:2=4\)

c) \(\left(2x-14\right)^7=128=2^7\)

\(2x-14=2\)

\(2x=14+2=16\)

\(x=16:2=8\)

d) \(x^4\cdot x^5=5^3\cdot5^6=5^4\cdot5^5\)

\(x=5\)

e) \(3\cdot\left(x+2\right):7\cdot4=120\)

\(x+2=120:3\cdot7:4\)

\(x+2=70\)

\(x=70-2=68\)

Lời giải:

a. $(x-1)^3=8=2^3$
$\Rightarrow x-1=2$

$\Rightarrow x=3$

b. $7^{2x-6}=49=7^2$
$\Rightarrow 2x-6=2$

$\Rightarrow 2x=8$

$\Rightarrow x=4$

c. $(2x-14)^7=128=2^7$

$\Rightarrow 2x-14=2$

$\Rightarrow 2x=16$

$\Rightarrow x=18$

d.

$x^4.x^5=5^3.5^6$

$x^9=5^9$

$\Rightarrow x=5$

e. 

$3(x+2):7=120:4=30$

$3(x+2)=30.7=210$

$x+2=210:3=70$

$x=70-2=68$

Ta có :

\(P=\left(x-4\right)^{\left(x-5\right)^{\left(x-6\right)^{\left(x+6\right)^{\left(x+5\right)}}}}\)

Mà : x=7

 \(P=\left(7-4\right)^{\left(7-5\right)^{\left(7-6\right)^{\left(7+6\right)^{\left(7+5\right)}}}}\)

\(P=9\)

Ta có P= (7-4)\(^{\left(7-5\right)^{\left(7-6\right)^{^{\left(7+6^{\left(7+5\right)}\right)}}}}\)
P=9