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a) \(2^5\cdot8^4\\ =2^5\cdot\left(2^3\right)^4\\ =2^5\cdot2^{12}\\ =2^{17}\)
b) \(25^6\cdot125^3\\ =\left(5^2\right)^6\cdot\left(5^3\right)^3\\ =5^{12}\cdot5^9\\ =5^{21}\)
c) \(625^3:25^7\\ =\left(5^4\right)^3:\left(5^2\right)^7\\ =5^{12}:5^{14}\\ =5^{-2}=\frac{1}{5^2}\)
d) \(4^{10}\cdot2^{30}\\ =\left(2^2\right)^{10}\cdot2^{30}\\ =2^{20}\cdot2^{30}\\= 2^{50}\)
e) \(9^{25}\cdot27^4\cdot81^3\\ =\left(3^2\right)^{25}\cdot\left(3^3\right)^4\cdot\left(3^4\right)^3\\ =3^{50}\cdot3^{12}\cdot3^{12}\\ =3^{74}\)
a/ (26.16) :42
=(26.22) :(22)2
=28 : 24=24=16
b/ (510:625) : 25
= (510:54) :52
=56 : 52=53=625
c/ (81.243):3
= (34.35) :3
= 39 :3=38 =6561
\(A=8^2.32^4=2^6.2^{20}=2^{26}\)
\(\Rightarrow2^{26}\)
\(B=27^3.9^4.243=3^9.3^8.3^5=3^{22}\)
\(\Rightarrow3^{22}\)
TL
a . x ∈ ∅ b . x=-10, x=-5177/5000, x=-10173/10000.
HT
a. =(54:5):(52.5)
=55:53
=52
b.= (34.33.32):(35.3)
=39:36
=33
d. = 8.125.8.25.8.5.25.2.5
= 23.53.23.52.23.5.52.2.5
=210.59
đúng nha
a; ( 625 : 5) : ( 125 . 5)
= ( 5^4 : 5) : ( 5^3 . 5)
= 5^3 : 5^4
= 1/5
b; (8 1 . 27 . 9 ) : ( 243 . 3)
= ( 3^4 . 3^3 . 3^2) : ( 3^4 . 3)
= 3^9 : 3^ 5
=3^4
c, 1000 x 200 x 40 x 25
= 1000 x ( 40x 250) x 200
= 1000 x 10000 x 200
= 2000000000
a) \(8^4.16^5\)
\(=\left(2^3\right)^4.\left(2^4\right)^5\\ =2^{3.4}.2^{4.5}\\ =2^{12}.2^{20}\\ =2^{12+20}\\ =2^{32}\)
b) \(5^{40}.125^2.625^3\)
\(=5^{40}.\left(5^3\right)^2.\left(5^4\right)^3\)
\(=5^{40}.5^{3.2}.5^{4.3}\)
\(=5^{40}.5^6.5^{12}\)
\(=5^{40+6+12}\)
\(=5^{58}\)
c) \(27^4.81^{10}\)
\(=\left(3^3\right)^4.\left(3^4\right)^{10}\)
\(=3^{3.4}.3^{4.10}\)
\(=3^{12}.3^{40}\)
\(=3^{52}\)
d) \(10^3.100^5.1000^4\)
\(=10^3.\left(10^2\right)^5.\left(10^3\right)^4\)
\(=10^3.10^{2.5}.10^{3.4}\)
\(=10^3.10^{10}.10^{12}\)
\(=10^{3+10+12}\)
\(=10^{25}\)
`@` `\text {Ans}`
`\downarrow`
`a,`
`4*8`
`= 2^2*2^3`
`=`\(2^{2+3}=2^5\)
`b,`
`4^5*4^4*4`
`=`\(4^{5+4+1}=4^{10}\)
`c,`
\(x^5\cdot x=x^{5+1}=x^6\)
`d,`
\(9\cdot27=3^2\cdot3^3=3^{2+3}=3^5\)
`e,`
\(243\div81=3^5\div3^4=3\)
`g,`
\(625\div25=5^4\div5^2=5^2\)
`@` `\text {Kaizuu lv uuu}`
a) \(4\cdot8=2^2\cdot2^3\)
\(=2^{2+3}=2^5=32\)
b) \(4^5\cdot4^4\cdot4\)
\(=4^{5+4+1}=4^{10}\)
c) \(x^5\cdot x\)
\(=x^{5+1}=x^6\)
d) \(9\cdot27=3^2\cdot3^3\)
\(=3^{2+3}=3^5\)
e) \(243:81=3^5:3^4\)
\(=3^{5-4}=3^1=3\)
g) \(625:25=5^4:5^2\)
\(=5^{4-2}=5^2=25\)