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Ta có :

a) \(\frac{21^{30}}{63^{15}}=\frac{\left(21^2\right)^{15}}{63^{15}}=\left(\frac{21^2}{63}\right)^{15}\)

b) \(\frac{28^9.30^9}{105^9}=\frac{\left(28.30\right)^9}{105^9}=\frac{840^9}{105^9}=\left(\frac{840}{105}\right)^9=8^9\)

13 tháng 7 2015

a) \(8^{15}.4^{13}=\left(2^3\right)^{15}.\left(2^2\right)^{13}=2^{45}.2^{26}=2^{71}\)

b) \(\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{4}\right)^{28}=\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{2^2}\right)^{28}=\frac{1}{2^{18}}.\frac{1}{2^{56}}=\frac{1}{2^{74}}=\left(\frac{1}{2}\right)^{74}\)

c) \(9^{12}.27^{10}=\left(3^2\right)^{12}.\left(3^3\right)^{10}=3^{24}.3^{30}=3^{54}\)

13 tháng 7 2015

a) = (23)15. (22)13 = 245.226 = 271

b) = \(\left(\frac{1}{2}\right)^{18}.\left(\left(\frac{1}{2}\right)^2\right)^{28}=\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{2}\right)^{56}=\left(\frac{1}{2}\right)^{18+56}=\left(\frac{1}{2}\right)^{74}\)

c) = (32)12.(33)10 = 324.330 = 324+30 = 354

18 tháng 8 2021

a. 82. 324 = 26. 220 = 226

b. 273. 94. 243 = 39. 38. 35 = 322

c. 5 .125 . 625 = 5 . 53. 54 = 58

d.10 . 100 . 1000 = 10 . 102. 103 = 106

e. 84. 165. 32 = 212. 220. 25 = 237

f. 274 . 8110 = 312. 340 = 352

23 tháng 6 2021

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13 tháng 9 2021

\(\frac{8^{11}.3^{17}}{27^{10}.9^{15}}=\frac{8^{11}.3^{17}}{3^{30}.3^{30}}=\frac{8^{11}}{3^{13}.3^{30}}=\frac{8^{11}}{3^{43}}\)

\(\frac{\left(5^4-5^3\right)^3}{125^4}=\frac{[\left(5-1\right).5^3]^3}{5^{12}}=\frac{\left(4.5^3\right)^3}{5^{12}}=\frac{64.5^9}{5^{12}}=\frac{64}{5^3}=\left(\frac{4}{5}\right)^3\)

\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+6^{20}}{6^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{30}\right)}{3^{20}.\left(2^{20}-2+3^{20}\right)}=\frac{2^{20}}{3^{20}}=\left(\frac{2}{3}\right)^{20}\)

Bài 1: 

a) \(4^8\cdot2^{20}=\left(2^2\right)^8\cdot2^{20}=2^{36}\)

 \(64^3\cdot4^5=\left(2^6\right)^3\cdot\left(2^2\right)^5=2^{18}\cdot2^{10}=2^{28}\)

\(y\cdot y^7=y^{1+7}=y^8\)

\(a^n\cdot a^2=a^{n+2}\)

Bài 1:

b) \(10^8:2^8=5^8\)

\(17^8:17^5=17^3\)

\(2^{25}:32^4=2^{25}:2^{20}=2^5\)

\(19^4:9^4=\left(\dfrac{19}{9}\right)^4\)

31 tháng 7 2019

\(4^{10}\cdot8^{15}\)

\(=\left(2^2\right)^{10}\cdot\left(2^3\right)^{15}\)

\(=2^{20}\cdot2^{45}\)

\(=2^{30+45}\)

\(=2^{75}\)

\(a;4^{10}\cdot8^{15}=2^{20}\cdot2^{45}=2^{65}\)

\(b;4^{15}\cdot5^{30}=2^{30}\cdot5^{30}=10^{30}\)

a) 158 x 94

= 158 x ( 32 )4

= 158 x 38

= ( 15 x 3 )8 = 458

b) 49 : 527

= 49 : ( 53 ) 9

= 49 : 1259

\(\left(\frac{4}{125}\right)^9\)

c) 2010 : 220

= 2010 : ( 22 )10

= 2010 : 410 = ( 20 : 4 ) 10 = 510

d) 275 : ( -7 ) 15

= 275 : [ ( - 7 )3 ]5

= 275 : ( - 21 )5

\(\left(\frac{27}{-21}\right)^5=\left(\frac{9}{-7}\right)^5\)

Cbht