Tính hợp lý (4^5x15^6+25^5x2^8):(2^8x5^4+5^7x2^5)
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`a, 4/9 + 2/5 + 5/9= (4/9 +5/9) + 2/5= 1 + 2/5= 5/5 + 2/5= 7/5`
`b, 6/13 + 5/8 + 7/13=(6/13 + 7/13) + 5/8=1+5/8= 8/8 + 5/8= 13/8`
`c, 5/11 + 6/25 + 66/121 = ( 5/11 + 66/121 ) + 6/25=1 + 6/25 = 25/25 + 6/25 = 31/25`
`d, 1/2 + 1/3 + 1/4 + 1/6 + 1/12 + 1/24= (1/2 + 1/4) +(1/3 + 1/6) + (1/12 + 1/24)= 3/4 + 1/2 + 1/8= 6/8 + 4/8 + 1/8= 11/8`
`@ yl`
\(2\times3\times5+25\times8\times4+70+4\times2\times25\)
\(=15\times2+100\times8+70+100\times2\)
\(=30+800+70+200\)
\(=\left(30+70\right)+\left(800+200\right)\)
\(=100+100\times10\)
\(=100+1000\)
\(=1100\)
\(D=\frac{4^7.2^8}{3.2^{15}.16^2+5.2.\left(2^{10}\right)^2}\)
\(=\frac{2^{14}.2^8}{3.2^{15}.2^8+5.2.2^{20}}\)
\(=\frac{2^{22}}{3.2^{23}+5.2^{21}}\)
\(=\frac{2^{22}}{2^{21}.\left(2^2.3+5\right)}\)
\(=\frac{2}{2^2.3+5}\)
\(=\frac{2}{17}\)
\(D=\frac{\left(2^2\right)^7.2^8}{3.2^{15}.\left(2^4\right)^2+5.2^2.2^{20}}\)
\(=\frac{2^{14}.2^8}{3.2^{15}.2^8+5.2^{22}}\)
\(=\frac{2^{22}}{3.2^{23}+5.2^{22}}\)
\(=\frac{2^{22}}{2^{22}\left(3.2+5\right)}=\frac{1}{11}\)
\(1\frac{4}{25}+\frac{7}{21}-\frac{4}{25}+0,5+\frac{14}{21}\)
\(=\left(1\frac{4}{25}-\frac{4}{25}\right)+\left(\frac{7}{21}+\frac{14}{21}\right)+0,5\)
\(=1+0+0,5\)
\(=1,5\)
a, 10 -12 - 8
= 10 - (12 + 8 )
= 10 - 20 = -10
b, 4-(-15)-5+6
= 4+15-5+6
= (4+6) + (15-5)
= 10+10=20
c, 2-12-4-6
= (2-12)-(4+6)
= (-10) - 10
=-20
d, -45-5-(-12)+8
= -45-5+12+8
= [(-45)-5]+(12+8)
= (-50)+20
= -30
\(a.10-12-8\\ =10+\left(-12-8\right)\\ =10+\left(-20\right)=-10\\ b.4-\left(-15\right)-5+6\\ =4+5-5+6\\ =\left(4+6\right)+\left(15-5\right)\\ =10+10=20\\ c.2-12-4-6\\ =\left(2-12\right)+\left(-4-6\right)\\ =-10+\left(-10\right)=-20\\ d.-45-5-\left(-12\right)+8\\ =-45-5+12+8\\ =\left(-45-5\right)+\left(12+8\right)\\ =-50+20=-30\)
\(\frac{3^2.9^3.25^2.12^6}{3^{15}.5^4.6^3.4^2}=\frac{3^2.3^{2.3}.5^{2.2}.3^6.4^6}{3^{15}.5^4.2^3.3^3.2^{2.2}}=\frac{3^2.3^6.3^6.5^4.2^{2.6}}{3^{15}.3^3.5^4.2^3.2^4}=\frac{3^{14}.2^{12}.5^4}{3^{18}.5^4.2^7}=\frac{2^5}{3^4}=\frac{32}{81}\)