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( 3x - 1 )3 = 125
( 3x - 1 )3 = 53
=> 3x - 1 = 5
3x = 6
x = 2
( 10 + x ) : 25 = 30 . 22
( 10 + x ) : 25 = 4
10 + x = 100
x = 90
\(125=5^3\)
\(25^2=\left(5^2\right)^2=5^{2.2}=5^4\)
\(\left(5^3\right)^2=5^{3.2}=5^6\)
\(125^5=\left(5^3\right)^5=5^{3.5}=5^{15}\)
\(625^4=\left(5^4\right)^4=5^{4.4}=5^{16}\)
\(125.5^2=5^3.5^2=5^{3+2}=5^5\)
125 = 53
252 = (52)2 = 54
(53)2 = 56
1255 = ( 53)5 = 515
6254 = (54)4 = 516
125 . 52 = 53 . 52 = 55
a. 25 . 84 = 25 . 212 = 217
b. 256 . 1253 = 512 . 59 = 521
c. 32 . 95 = 32 . 310 = 312
d. 253 . 1254 = 56 . 512 = 518
e. 42 . 52 = 202
a) $125^3:25^4=(5^3)^3:(5^2)^4=5^9:5^8=5^1$
$16^4:4^2=(4^2)^4:4^2=4^8:4^2=4^6$
$27^8:9^4=(3^3)^8:(3^2)^4=3^{24}:3^8=3^{16}$
$125^5:25^3=(5^3)^5:(5^2)^3=5^{15}:5^6=5^9$
$4^{14}:5^{28}=(2^2)^{14}:5^{28}=2^{28}:5^{28}=(\dfrac{2}{5})^{28}$
b) $12^n:2^{2n}=12^n:(2^2)^n=12^n:4^n=3^n$
$64^4.16^5.4^{20}=(4^3)^4.(4^2)^5.4^{20}=4^{12}.4^{10}.4^{20}=4^{42}$
(52x.5x+2) : 25 = 1252
52x.5x+2 = 1252.25 = 56.52
52x+x+2 = 58
53x+2 = 58
=> 3x + 2 = 8
=> 3x = 6
=> x = 2
\(125^2\cdot25^3\cdot5^{2007}\)
\(=\left(5^3\right)^2\cdot\left(5^2\right)^3\cdot5^{2007}\)
\(=5^6\cdot5^6\cdot5^{2007}\)
\(=5^{2019}\)
\(B=\frac{125^2\cdot72^3:9^3}{4^3\cdot25^5\cdot5^5}=\frac{\left(5^3\right)^2\cdot\left(2^3\cdot3^2\right):\left(3^2\right)^3}{\left(2^2\right)^3\cdot\left(5^2\right)^5\cdot5^5}=\frac{5^6\cdot2^3\cdot3^2:3^6}{2^6\cdot5^{10}\cdot5^5}\)
tỰ TÍNH
a) 1252 . 82 - (24)2 + 59 : 1252
=(125 . 8)2 - 24.2 + 59 : (53)2
= 10002 - 28 + 59 : 56
= 1000000 - 256 + 53
= 999744 + 125
= 999869
b) Mình ko viết đầu bài đâu nhé
=(75 : 5)2 + (25 . 4)4 - 33 . 52
= 152 + 1004 - 27 . 25
= 15. 15 + 100 . 100 . 100 . 100 - 675
= 225 + 100000000 - 675
= 100000000 - (675 - 225)
= 100000000 - 450
= 99999550
=
( 3x - 2 )5 = 52 . 53
( 3x -2 )5 = 55
=> 3x-2=5
3x=5+2
3x=7
x=\(\frac{7}{3}\)
(3x-2)5=25×125
(3x-2)5=52×53
(3x-2)5=55
=>3x-2=5
3x =7
x =7÷3
x = 7/3