Tìm gia trị biểu thức:
9^12 . 3^5 + 9^15 / ( 2 . 27 )^5 . 3^14
5^4 + 2^2 . 5^ 2 - 125 / 2^3 . 3
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a) 2^7 . 9^3 / 6^5 . 8^2
= 2^7 . 3^9 / 2^5 . 3^5 . 2^6
= 2^-4 . 3^4
\(1,\\ a,\Leftrightarrow4^{5-x}=4^2\Leftrightarrow5-x=2\Leftrightarrow x=3\\ b,\Leftrightarrow\left[{}\begin{matrix}x-1=5\\x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\\ c,\Leftrightarrow2x+1=3\Leftrightarrow x=2\\ 2,\\ a,3^{100}=\left(3^2\right)^{50}=9^{50}\\ b,2^{98}=\left(2^2\right)^{49}=4^{49}< 9^{49}\\ c,5^{30}=5^{29}\cdot5< 6\cdot5^{29}\\ d,3^{30}=\left(3^3\right)^{10}=27^{10}>8^{10}\\ 4,\\ a,\Leftrightarrow5\left(x-10\right)=10\\ \Leftrightarrow x-10=2\Leftrightarrow x=12\\ b,\Leftrightarrow3\left(70-x\right)+5=92\\ \Leftrightarrow3\left(70-x\right)=87\\ \Leftrightarrow70-x=29\\ \Leftrightarrow x=41\\ c,\Leftrightarrow16+x-5=315-230=85\\ \Leftrightarrow x=74\\ d,\Leftrightarrow2^x-5+74=707:\left(16-9\right)=707:7=101\\ \Leftrightarrow2^x=32=2^5\\ \Leftrightarrow x=5\)
a) (125 -679 + 145 ) - ( 125 - 679 )=125 -679+145-125+679=145
b)(x - 29 ) - ( 17 - 38 ) = -9
<=> x-29 -17+38=-9
<=>x=-1
c)( x + 5 ) + ( x - 9 ) = x + 2
<=>x+5+x-9=x+2
<=>x+x-x=2+9-5
<=>x=6
d) ( 27 - x )+ ( 15 + x ) = x - 24
<=> 27-x+15+x-x=-24
<=> -x=-66
<=>x=66
e) -359 + 181 + ( -123 ) + 350 + ( -172 ) = (181 +350)-(359+172) -123 =531-531-123=-123
f) 13 - 12 + 11 + 10 - 9 + 8 - 7 -6 + 5 - 4 + 3 + 2 -1=( 13 - 12) +11 + (10 - 9)+(8-7)-6+(5-4)+3+(2-1)=1+11+1+1-6+1+3+1=13
a, (125 -679 + 145 ) - ( 125 - 679 )
= 125 - 679 + 145 - 125 + 679
= ( 125 - 125 ) + ( -679 + 679 ) + 145
= 0 + 0 +145
= 145
b, (x - 29 ) - ( 17 - 38 ) = -9
x - 29 - 17 + 38 = -9
x - 29 - 17 = -9 - 38
x - 29 - 17 = -47
x - 29 = -47 + 17
x - 29 = -30
x = -30 + 29
x = -1
Vậy x = -1
c, ( x + 5 ) + ( x - 9 ) = x + 2
x + 5 + x - 9 = x + 2
x - x + 14 = x + 2
14 = x + 2
x = 14 - 2
x = 12
Vậy x = 12
d, ( 27 - x )+ ( 15 + x ) = x - 24
27 - x + 15 + x = x - 24
42 + ( -x + x ) = x - 24
42 = x - 24
x = 24 + 42
x = 66
Vậy x = 66
e, -359 + 181 + ( -123 ) + 350 + ( -172 )
= ( -359 + 350 ) + [ 181 + ( -172 ) ] + ( -123)
= (-9) + 9 + ( -123 )
= 0 + ( -123)
= (-123)
g , 13 - 12 + 11 + 10 - 9 + 8 - 7 -6 + 5 - 4 + 3 + 2 -1
= ( 13 - 12 ) + ( 10 - 9 ) + ( 8 - 7 ) + ( 5 - 4 ) + ( 2 - 1 ) + ( 11 - 6 + 3)
= 1 + 1 + 1 + 1 + 1 + 8
= 1. 5 + 8
= 5 + 8
= 13
1/ \(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\frac{5^{20}.3^{29}-3^{31}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{19}}=\frac{3^{29}.5^{18}.\left(25-9\right)}{3^{29}.5^{18}.\left(7-5\right)}=\frac{16}{2}=8\)
CÁC BÀI CÒN LẠI TƯƠNG TỰ HẾT NHÉ E
a, \(\dfrac{4^2.4^3}{2^{10}}=\dfrac{4^5}{2^{10}}=\dfrac{\left(2^2\right)^5}{2^{10}}=\dfrac{2^{10}}{2^{10}}=1\)
b, \(\dfrac{2^7.9^3}{6^5.8^2}=\dfrac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\dfrac{2^7.3^6}{2^5.3^5.2^6}=\dfrac{3}{2^4}=\dfrac{3}{16}\)
c, \(\dfrac{9^7.5^6.125^9}{15^{15}.5^{18}}=\dfrac{3^{21}.5^6.5^{27}}{5^{15}.3^{15}.5^{18}}=\dfrac{3^{21}.5^{33}}{3^{15}.5^{33}}=3^6=729\)
d, \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^9.\left(1+3.5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2.16}{3^2.5}=\dfrac{32}{45}\)
Chúc bạn học tốt!!!