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1. a) 3^2 .2^2 .2^4 = 3^2. 2^(2+4)=3^2. 2^6
b) 10^2. 10^3.10^5= 10^(2+3+5)= 10^10
c) x.x^5=x^(1+5)=x^6
d) a^3 .a^2 ,a^5= a^(3+2+5)= a^10
2. a) 2^3 và 3^2 . Ta có: 2^3 = 8, 3^2=9 => 2^3 < 3^2
b) 2^4 và 4^2. Ta có: 2^4= 16, 4^2=16 => 2^4 = 4^2
c) 2^5 và 5^2. Ta có: 2^5= 32, 5^2=25 => 2^5 > 5^2
d) 2^100 và 100. => 2^100 > 100
3. a) 3^8:3^4= 3^(8-4)=3^4
b) 10^8:10^2=10^(8-6)=10^2
c) a^6: a (a#0) = a^(6-1)=a^5
a, \(5^x=625\Rightarrow5^x=5^4\Rightarrow x=4\)
b, \(4^{2x-6}=1\Rightarrow4^{2x-6}=4^0\)
\(\Rightarrow2x-6=0\Rightarrow x=3\)
c, \(\left(3x-1\right)^3=8\Rightarrow3x-1=2\)
\(\Rightarrow x=1\)
d, \(49.7^n=2401\Rightarrow7^{n+2}=7^4\)
\(\Rightarrow n+2=4\Rightarrow n=2\)
e, \(x^4.x-27.x=0\)
\(\Rightarrow x\left(x^4-27\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^4-27=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=\pm\sqrt[4]{27}\end{cases}}\)
f, \(\left(x-6\right)^3=\left(x-6\right)^2\)
\(\Rightarrow\left(x-6\right)^3-\left(x-6\right)^2=0\)
\(\Rightarrow\left(x-6\right)^2\left(x-6-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-6=0\\x-7=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=6\\x=7\end{cases}}\)
Chúc bạn học tốt!!!
\(a,5^x=625\) \(b,4^{2x-6}=1\)
\(\Rightarrow5^x=5^4\) \(\Rightarrow2x-6=0\) (Vì mọi số mũ không bằng 1)
\(\Rightarrow x=4\) \(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
\(c,\left(3x-1\right)^3=8\) \(d,49.7^n=2401\)
\(\Rightarrow\left(3x-1\right)^3=2^3\) \(\Rightarrow7^n=2401:49\)
\(\Rightarrow3x-1=2\) \(\Rightarrow7^n=49\)
\(\Rightarrow3x=3\) \(\Rightarrow7^n=7^2\)
\(\Rightarrow x=1\) \(\Rightarrow n=2\)
\(e,x^4.x-27.x=0\)
\(\Rightarrow x.\left(x^4-27\right)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\x^4-27=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x^4=27\end{cases}}}\)
\(f,\left(x-6\right)^3=\left(x-6\right)^2\)
\(\Rightarrow x.\left(x^4-27\right)=0\) \(\Rightarrow\hept{\begin{cases}\left(x-6\right)^3=\left(x-6\right)^2\\\left(x-6\right)^3=\left(x-6\right)^2\end{cases}\Rightarrow\hept{\begin{cases}\left(x-6\right)^3:\left(x-6\right)^2=1\\\left(x-6\right)^3-\left(x-6\right)^2=0\end{cases}\Rightarrow}\hept{\begin{cases}x-6=1\\x-6=0\end{cases}}\Rightarrow\hept{\begin{cases}x=7\\x=6\end{cases}}}\)
a) a mũ 4 chia a = a mũ 3
b) ( 16 mũ 2 ) / ( 4 mũ 2 )
= ( 16 / 4 ) mũ 2
= 4 mũ 2
= 16
c) ( 25 mũ 2 ) / ( 5 mũ 2 )
= ( 25 / 5 ) mũ 2
= 5 mũ 2
= 25
\(a^4:a=a^3\)
\(16^2:4^2=\left(16:4\right)^2=4^2=16\)
\(25^2:5^2=\left(25:5\right)^2=5^2=25\)
a: \(=\dfrac{-28}{36}+\dfrac{15}{36}-\dfrac{26}{36}=\dfrac{-39}{36}=\dfrac{-13}{12}\)
b: \(=\dfrac{11}{9}\left(\dfrac{15}{4}-\dfrac{7}{4}-\dfrac{5}{4}\right)=\dfrac{11}{9}\cdot\dfrac{3}{4}=\dfrac{11}{12}\)
c: \(=15+\dfrac{9}{7}+6+\dfrac{2}{3}-5-\dfrac{5}{9}\)
\(=16+\dfrac{88}{63}=\dfrac{1096}{63}\)
d: \(=\dfrac{5}{6}-\dfrac{1}{3}+\dfrac{2}{18}\)
\(=\dfrac{15-6+2}{18}=\dfrac{11}{18}\)
a) \(2^3=2.2.2=8\)
\(2^4=2.8=16\)
\(2^5=2.16=32\)
\(2^6=2.32=64\)
\(2^7=2.64=128\)
\(2^8=2.128=256\)
\(2^9=2.256=512\)
\(2^{10}=2.512=1024\)
b) \(4^2=4.4=16\)
\(4^3=16.4=64\)
\(4^4=64.4=256\)
Còn lại tương tự
a) \(2^{3+4+5+6+7+8+9+10}=2^{52}\)
b) \(3^{14}\)\(=4782969\)
c) \(4^9\)\(=262144\)
d) \(5^9\)\(=1953125\)
e) \(6^9\)\(=10077696\)
K mk nha, mk nhanh nha
Bài 2:
b: x+25%x=-1,25
=>1,25x=-1,25
hay x=-1
c: x-75%x=1/4
=>1/4x=1/4
hay x=1
Bài 2:
a: =3/2-11/4=6/4-11/4=-5/4
b: =-49/6-17/2=-49/6-51/6=-100/6=-50/3
a, \(6^5:6^2=6^{5-2}=6^3\)
b, \(2^3.4=2^3.2^2=2^{3+2}=2^5\)
c, \(5^5:25=5^5:5^2=5^{5-2}=5^3\)
d, \(49^3:7^4=7^6:7^4=7^{6-4}=7^2\)
e, \(a^9:a=a^{9-1}=a^8\)\(\left(a\ne0\right)\)
Chúc bạn học tốt!!!
a,65:62=65-2=63
b,23x4= 25
c,55:25=55:55=1
d,493:74= 72
e, a9:a=a9-1=a8