Question

14.28-14.29(в,г)Прошу помогите

Answer 1

(14.28)
в)
$\frac{36^3*15^2}{18^4*10^3}=\frac{(3^2*2^2)^{3}*(3*5)^2}{(3^2*2)^4*(2*5)^{3}}=\frac{3^6*2^6*3^2*5^2}{3^8*2^4*2^3*5^3}=3^{6+2-8}*2^{6-4-3}*5^{2-3}=\\=3^0*2^{-1}*5^{-1}=1*\frac{1}{2*5}=\frac{1}{10}=0.1$


г)
$\frac{22^4*3^3}{6^2*121^2}=\frac{(11*2)^4*3^3}{(2*3)^2*(11^2)^2}=\frac{11^4*2^4*3^3}{2^2*3^2*11^4}=11^{4-4}*2^{4-2}*3^{3-2}=\\=11^0*2^2*3^1=1*4*3=12$




(14.29)
в)
$\frac{108*6^7-108*6^6}{216^3-36^4}=\frac{(6^2*3)*6^7-(6^2*3)*6^6}{(6^3)^3-(6^2)^4}=\frac{6^9*3-6^8*3}{6^9-6^8}=\frac{6^8(3*6^{9-8}-3*6^{8-8})}{6^8(6^{9-8}-6^{8-8})}=\\=\frac{18-3}{6-1}=\frac{15}{3}=5$

г)
$\frac{(3^{15}+3^{13})*2^9}{(3^{14}+3^{12})*1024}=\frac{3^{13}(3^{15-13}+3^{13-13})*2^9}{3^{12}(3^{14-12}+3^{12-12})*2^{10}}=3^{13-12}*2^{9-10}*\frac{(3^2+3^0)}{(3^2+3^0)}=\\=3^1*2^{-1}*1=\frac{3}{2}=0.5$

Answer 2

14.27
а)$13^6*2^6/26^5=26^6/26^5=26$
б)$7 ^{11} * 9^{11} /(63^5)^2= 63^{11} /63 ^{10} =63$
в)$2^8*3^6/(6^4)^2=2^8*3^6/2^8*3^8=1/3^2=1/9$
г)$12^6/3^5*4^5=12^6/12^5=12$
14.28
а)$25^3*14^2/49*10^6=5^6*2^2*7^2/7^2*2^6*5^6=1/2^4=1/16$
б)$12^2*35^3/28^2*15^4=4^2*3^2*5^3*7^3/4^2*7^2*3^4*5^4=7/3^2*5=7/45$
в)$36^3*15^2/18^4*10^3=18^3*2^3*3^2*5^2/18^4*2^3*5^3=3^2/18*5=9/90$=1/10
г)$22^4*3^3/6^2*11^2=2^4*11^4*3^3/3^2*2^2*11^2=11^2*2^2*3=121*4*3$=1452
14.29
а)$(2* 3^{20} -5* 3^{19} )/9^9= 3^{19}(6-5)/ 3^{18} =3$
б)$(3* 2^{20} +7* 2^{19})*52/(13*8^4)^2= 2^{19} *(6+7)*13*2^2/13^2* 2^{24}$=1/2³=1/8
в)$(108*6^7-108*6^6)/(216^3-36^4)=108*6^6*(6-1)/(6^9-6^8)=$$6^3*6^6*5/6^8*(6-1)=6$
г)$( 3^{15}+ 3^{13} )*2^9/( 3^{14} +3 ^{12})*1024= 3^{13} *(9+1)*2^9/ 3^{12} *(9+1)* 2^{10}$=3/2
14.30
a)$2 ^{(2x+1)}$ /3^x=4 20/27[/tex]
$2*(4/3)^x=128/27$
$(4/3)^x=64/27$
x=3
б)$5*25^x/ 2^{4x} =7 13/16$
$5*(25/16)^x=125/16$
$(25/16)^x=25/16$
x=1