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Bài 1:
a: \(=\dfrac{-1}{8}+1-\dfrac{9}{4}-1\)
\(=\dfrac{-1}{8}-\dfrac{18}{8}=\dfrac{-19}{8}\)
b: \(=4\cdot1-2\cdot\dfrac{1}{4}+3\cdot\dfrac{-1}{2}+1\)
\(=4-\dfrac{1}{2}-\dfrac{3}{2}+1\)
=5-2
=3
a: \(\Leftrightarrow4^x\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)=4^8\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)\)
=>4^x=4^8
=>x=8
b: \(\Leftrightarrow2^x\cdot\dfrac{1}{2}+2^x\cdot2=2^{10}\left(2^2+1\right)\)
=>2^x=2^11
=>x=11
c: =>1/6*6^x+6^x*36=6^15(1+6^3)
=>6^x=6*6^15
=>x=16
d: \(\Leftrightarrow8^x\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)=8^9\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)\)
=>x=9
b) \(\dfrac{7}{15}-\dfrac{9}{19}\)\(-\dfrac{-8}{15}-\dfrac{10}{19}\)
=\(\left(\dfrac{7}{15}-\dfrac{8}{15}\right)\) \(-\left(\dfrac{9}{19}-\dfrac{10}{19}\right)\)
= \(-\dfrac{1}{15}\) - \(\left(-\dfrac{1}{19}\right)\)
\(=-\dfrac{1}{15}\) + \(\dfrac{1}{19}\)
= \(-\dfrac{4}{285}\)
c) \(1\dfrac{1}{3}\) \(\div\) \(\dfrac{4}{5}\) + 2\(\dfrac{2}{3}\) \(\div\)\(\dfrac{4}{5}\)
= \(\left(1\dfrac{1}{3}+2\dfrac{2}{3}\right)\) \(\div\dfrac{4}{5}\)
= \(\left[\left(1+2\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\right]\) \(\div\dfrac{4}{5}\)
= ( 3 + 1 ) \(\div\dfrac{4}{5}\)
= 4 \(\div\dfrac{4}{5}\)
= \(\dfrac{4.5}{4}\)
= 5
a) 4. ( 1.1/4)2 + [(3/4)2 : (5/4)3] : (3/2)3
= 4.1/16 + [9/16 : 125/64] : 27/8
= \(\frac{1}{4}+\frac{9}{16}:\frac{125}{64}:\frac{27}{8}=\frac{1}{4}+\frac{36}{125}:\frac{27}{8}\)
= \(\frac{1}{4}+\frac{36}{125}.\frac{8}{27}\)
=\(\frac{1}{4}+\frac{32}{375}=\frac{375}{1500}+\frac{128}{1500}=\frac{503}{1500}\)
b] = 2^3 + 3 x 1 - 1 + ( 2^2 x 2 ) x 2^3
= 2^3 + 3 - 1 + 2^3 x 2^3
= 2^3 + 2 + 2^6 = 74
a] = 4 x ( 1/4 )2 + ( 32/42 : 53/43 ) : 27/8
= 4 x 1/16 + ( 32 x 4/53 ) x 8/27
= 1/4 + 36/53 x 8/27 = 1/4 + 4/125 x 8/3 = 503/1500 sấp sỉ 0,335333
a: \(A=\left(5xy-2xy+1.3xy\right)+3x-2y-3.5y^2\)
\(=4.3xy+3x-2y-3.5y^2\)
b: \(B=\left(\dfrac{1}{2}ab^2-\dfrac{1}{2}ab^2-\dfrac{7}{8}ab^2\right)+\left(\dfrac{3}{4}a^2b-\dfrac{3}{8}a^2b\right)\)
\(=-\dfrac{7}{8}ab^2+\dfrac{3}{8}a^2b\)
c: \(C=\left(2a^2b+5a^2b\right)+\left(-8b^2-3b^2\right)+\left(5c^2+4c^2\right)\)
\(=7a^2b-11b^2+9c^2\)
a: \(=-10bx^3y^2\)
b: \(\dfrac{-4}{5}ab^2c\cdot\left(-20\right)a^4bx=16a^5b^3c\cdot x\)
c: \(=8\cdot\dfrac{1}{4}\cdot a^3\cdot b^2c^4=2a^3b^2c^4\)
d: \(=2ab\cdot\dfrac{4}{3}a^2\cdot b^4\cdot7abc=\dfrac{56}{3}a^4b^6c\)
1) Tính
a) 253 : 52 = (52)3 : 52 = 56 : 52 = 54 = 625
\(b)\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^6=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^6=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^{12}=\left(\dfrac{3}{7}\right)^9\) d) 9 . 32 . \(\dfrac{1}{81}\) . 32 = 32 . 32 . \(\dfrac{1}{3^4}\) . 32 = 9
2) Tìm x thuộc Q, biết:
a) 3x + 2 = 27
=> 3x + 2 = 33
x + 2 = 3
x = 3 - 2
x = 1
b) \(\left(\dfrac{1}{2}x-3\right)^4=81\)
\(\Rightarrow\left(\dfrac{1}{2}x-3\right)^4=3^4\)
\(\dfrac{1}{2}x-3=3^{ }\)
\(\dfrac{1}{2}x=3+3\)
\(\dfrac{1}{2}x=9\)
\(x=9:\dfrac{1}{2}\)
\(x=18\)
c) \(\left(x-\dfrac{1}{2}\right)^3=-27\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\left(-3\right)^3\)
\(x-\dfrac{1}{2}=-3\)
\(x=-3+\dfrac{1}{2}\)
\(x=\dfrac{-5}{2}\)
d) 5 . 5x + 1 = 125
5x + 1 = 125 : 5
5x + 1 = 25
5x + 1 = 52
x + 1 = 2
x = 2 - 1
x = 1.
a,-8+4+1+1=-2
b,16+8-64=-32
-2
-32