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a)410. 815 = (22)10.(23)15
=220.245
=265
b) 415 . 530 = 415 . (52)15
= 415 . 2515
= (4.25)15
= 10015
c) 2716 : 910 = (33)16 : (32)10
=348 : 320
=328
d)A=\(\frac{72^3.54^2}{108^4}\)
TS:723.542=(2.2.2.3.3)3.(2.3.3.3)2
=23.23.23.33.33.22.32.32.32
=23+3+3+2.33+3+2+2+2
=211.312
MS:1084=(2.2.3.3.3)4
=24. 24.34.34.34
=24+4 . 34+4+4
=28 . 312
\(\Rightarrow\)A=\(\frac{2^{11}.3^{12}}{2^8.3^{12}}\) = 23=8
e)B=\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
TS:310 .11 + 310 .5 = 310 . (11+5)
= 310 . 16
= 310. 24
\(\Rightarrow\)B=\(\frac{3^{10}.2^4}{3^9.2^4}\) = 31=3
Giải:A=723.542/(54.2)4=723.542/544.24=723/542.24=35.26/35.26=1. B=39.3.11+39.3.5/39.24=39.(33+15)/39.24=48/16=3. C=210.(13+65)/22.104=28.78/104=28.26.3/26.4=28.3/4=26.3=192. a)->2x=128:4=32.=>x=5(25=32) b)->2x+1=5(53=125)=>x=2. c)Ko có số nào ngoài 1 và 0 tồn tại dưới dạng(x-5)4=(x-5)6 ->Nếu x-5=0=>x=5 ->Nếu x-5=1=>x=6
0
( 2^3 x 3^2)^3 x ( 2 x 3^3 )^2 = 2^9 x 3^6 x 2^2 x 3^6 = 2^11 x 3^12
( 2^2 x 3^3 ) = 2^8 x 3^12 = 2^8 x 3^12
= 2^3 = 8
Trả lời:
a) \(4^{10}.8^{15}=\left(2^2\right)^{10}.\left(2^3\right)^{15}\)
\(=2^{20}.2^{45}\)
\(=2^{65}\)
\(a,4^{10}\cdot8^{15}=\left[2^2\right]^{10}\cdot\left[2\cdot2^2\right]^{15}=2^{20}\cdot2^{15}\cdot2^{30}=2^{20+15+30}=2^{65}\)
\(b,\frac{27^{16}}{3^{10}}=\frac{\left[3^3\right]^{16}}{3^{10}}=\frac{3^{48}}{3^{10}}=3^{48-10}=3^{38}\)
\(c,\frac{\left[2^9\cdot16+2^9\cdot34\right]}{2^{10}}=\frac{\left[2^9\left\{16+34\right\}\right]}{2^{10}}=\frac{2^9\cdot50}{2^{10}}=\frac{1}{2}\cdot50=25\)
\(d,\frac{3^4\cdot57-9^2\cdot21}{3^5}=\frac{3^4\cdot57-\left[3^2\right]^2\cdot21}{3^5}=\frac{3^4\cdot57-3^4\cdot21}{3^5}=\frac{3^4\left[57-21\right]}{3^5}=\frac{1}{3}\cdot36=12\)
a.
\(4^{10}\times8^{15}=\left(2^2\right)^{10}\times\left(2^3\right)^{15}=2^{20}\times2^{45}=2^{65}\)
b.
\(4^{15}\times5^{30}=\left(2^2\right)^{15}\times5^{30}=2^{30}\times5^{30}=\left(2\times5\right)^{30}=10^{30}\)
c.
\(\frac{27^{16}}{9^{10}}=\frac{\left(3^3\right)^{16}}{\left(3^2\right)^{10}}=\frac{3^{48}}{3^{20}}=3^{28}\)
d.
\(A=\frac{72^3\times54^2}{108^4}=\frac{\left(8\times9\right)^3\times\left(27\times2\right)^2}{\left(27\times4\right)^4}=\frac{\left(2^3\times3^2\right)^3\times\left(3^3\times2\right)^2}{\left(3^3\times2^2\right)^4}=\frac{2^9\times3^6\times3^6\times2^2}{3^{12}\times2^8}=2^3=8\)
e.
\(B=\frac{3^{10}\times11+3^{10}\times5}{3^9\times2^4}=\frac{3^{10}\times\left(11+5\right)}{3^9\times16}=\frac{3\times16}{16}=3\)
Chúc bạn học tốt
a)
\(4^{10}\cdot8^{15}=2^{20}\cdot2^{45}=2^{65}\)
b)
\(27^{16}\cdot9^{10}=3^{48}\cdot3^{20}=3^{68}\)
a) 410 . 815 = (22)10 . (23)15 = 220 . 245 = 265
b) 2716 . 910 = (33)16 .(32)10=348 . 320 = 368
c) \(\frac{2^{10}\cdot13+2^{10}\cdot65}{28\cdot104}=\frac{2^{10}\cdot13\cdot\left(1+5\right)}{2^5\cdot7\cdot13}=\frac{2^5\cdot6}{7}=\frac{192}{7}\)