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\(\frac{16}{2^n}=2\)
=> 2n=16:2
=> 2n=8
=> 2n=23
=> n=3
b;
\(\frac{\left(-3\right)^n}{81}=-27\)
\(\Rightarrow\left(-3\right)^n=-27.81\)
=> (-3)n=-2187
=> (-3)n=(-3)7
=> n=7
c ; \(8^n:2^n=4\)
\(\Rightarrow\left(8:2\right)^n=4\)
\(\Rightarrow\left(4\right)^n=4\)
Mà : 4=41
=> 4n=41
=> n=1
\(\frac{16}{2^n}=2\)
\(16:2^n=2\)
\(2^4:2^n=2\)
\(2^n=2^4:2\)
\(2^n=2^3\)
\(=>n=3\)
\(\frac{\left(-3\right)^n}{81}=-27\)
\(\left(-3\right)^n:81=-27\)
\(\left(-3\right)^n=-27\cdot81\)
\(\left(-3\right)^n=-2187\)
\(\left(-3\right)^n=\left(-3\right)^7\)
\(=>n=7\)
\(x^2\ge0\Rightarrow x^2+1\ge1>0\Rightarrow\left|x^2+1\right|=x^2+1\)
<=>\(x^2+1-\left|x^2-4\right|=1\Leftrightarrow x^2-\left|x^2-4\right|=0\Leftrightarrow x^2=\left|x^2-4\right|\)
+)\(x^2-4>0\Leftrightarrow x^2>4\Leftrightarrow x< -2;x>2\)
<=>\(x^2-4=x^2\Leftrightarrow0=4\) vô lý
+)\(x^2-4\le0\Leftrightarrow x^2\le4\Leftrightarrow-2\le x\le2\)
<=>\(4-x^2=x^2\Leftrightarrow4=2x^2\Leftrightarrow x^2=2\Leftrightarrow\orbr{\begin{cases}x=-\sqrt{2}\\x=\sqrt{2}\end{cases}}\)(nhận)
Vậy ...
(-10/3)5.(-6/5)4
= -10/3 . (-10/3)4 . (-6/5)4
= -10/3 . (-10/3.(-6/5)4
= -10/3. 44
= -10/3. 256
= -2560/3
\(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}\left(6-1\right)}\)
\(=\frac{2.6}{3.5}=\frac{4}{5}\)
a.
\(10^8\times2^8=\left(10\times2\right)^8=20^8\)
b.
\(10^8\div2^8=\left(10\div2\right)^8=5^8\)
c.
\(25^4\times2^8=\left(5^2\right)^4\times2^8=5^8\times2^8=\left(5\times2\right)^8=10^8\)
d.
\(15^8\times9^4=15^8\times\left(3^2\right)^4=15^8\times3^8=\left(15\times3\right)^8=45^8\)
e.
\(27^2\div25^3=\left(3^3\right)^2\div\left(5^2\right)^3=3^6\div5^6=\left(\frac{3}{5}\right)^6\)