Bài 5:
a) \(x:\left(-\dfrac{1}{2}\right)^3=-\dfrac{1}{2}\)
\(\Rightarrow x=\left(-\dfrac{1}{2}\right)^3\cdot\left(-\dfrac{1}{2}\right)\)
\(\Rightarrow x=\left(\dfrac{1}{2}\right)^4=\dfrac{1}{16}\)
b) \(\left(\dfrac{3}{4}\right)^5\cdot x=\left(\dfrac{3}{4}\right)^7\)
\(\Rightarrow x=\left(\dfrac{3}{4}\right)^7:\left(\dfrac{3}{4}\right)^5\)
\(\Rightarrow x=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}\)
c) \(\left(\dfrac{2}{3}\right)^5:x=\left(\dfrac{2}{3}\right)^3\)
\(\Rightarrow x=\left(\dfrac{2}{5}\right)^5:\left(\dfrac{2}{3}\right)^3\)
\(\Rightarrow x=\left(\dfrac{2}{5}\right)^2=\dfrac{4}{25}\)
d) \(\dfrac{25}{5^x}=5\)
\(\Rightarrow5^x\cdot5=25\)
\(\Rightarrow5^{x+1}=25\)
\(\Rightarrow5^{x+1}=5^2\)
\(\Rightarrow x+1=2\)
\(\Rightarrow x=2-1=1\)
e) \(\left(-\dfrac{1}{3}\right)^{x-5}=\dfrac{1}{81}\)
\(\Rightarrow\left(-\dfrac{1}{3}\right)^{x-5}=\left(-\dfrac{1}{3}\right)^4\)
\(\Rightarrow x-5=4\)
\(\Rightarrow x=4+5=9\)
g) \(\left(2x-3\right)^2=9\)
\(\Rightarrow\left(2x-3\right)=3^2\)
\(\Rightarrow2x-3=3\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=\dfrac{6}{2}=3\)
h) \(\left(x+5\right)^3=64\)
\(\Rightarrow\left(x+5\right)^3=4^3\)
\(\Rightarrow x+5=4\)
\(\Rightarrow x=4-5=-1\)
i) \(2^{3x+2}=4^{x+5}\)
\(\Rightarrow2^{3x+2}=\left(2^2\right)^{x+5}\)
\(\Rightarrow2^{3x+2}=2^{2x+10}\)
\(\Rightarrow3x+2=2x+10\)
\(\Rightarrow3x-2x=10-2\)
\(\Rightarrow x=8\)
k) \(5^{x+1}-5^x=500\)
\(\Rightarrow\left(5-1\right)\cdot5^x=500\)
\(\Rightarrow4\cdot5^x=500\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
4:
a: =(4/9+3/9)^2=(7/9)^2=49/81
b; =(5/10-6/10)^2=(-1/10)^2=1/100
c; =1/27*4+3/4
=4/27+3/4
=16/108+81/108=99/108
d: =7-1+1/18
=6+1/18
=109/18
e: =2+3=5
f: =3^9:3^7=3^2=9
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