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E= 29.26:213 = 29+6-13 = 22 = 4
F=35.27.26 = 35.33.26 = 38.26 = 419904
G=64.210 :214 = 26.210 :214 = 26+10-14 = 22 = 4
F=32.128:210 = 25.27:210 = 25+7-10 = 22 = 4
a) $3^8:3^6=3^{8-6}=3^2$
$19^7:19^3=19^{7-3}=19^4$
$2^{10}:8^3=2^{10}:(2^3)^3=2^{10}:2^9=2^{10-9}=2^1$
$12^7:6^7=(12:6)^7=2^7$
$27^5:81^3=(3^3)^5:(3^4)^3=3^{15}:3^{12}=3^{15-12}=3^3$
b) $10^6:10=10^{6-1}=10^5$
$5^8:25^2=5^8:(5^2)^2=5^8:5^4=5^{8-4}=5^4$
$4^9:64^2=4^9:(4^3)^2=4^9:4^6=4^{9-6}=4^3$
$2^25:32^4=2^{25}:(2^5)^4=2^{25}:2^{20}=2^{25-20}=2^5$
$18^3:9^3=(18:9)^3=2^3$
\(\cdot3^8:3^6=3^{8-6}=3^2\)
\(\cdot19^7:19^3=19^{7-3}=19^4\)
\(\cdot2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^9=2\)
\(\cdot12^7:6^7=\left(12:6\right)^7=2^7\)
\(\cdot27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)
\(\cdot10^6:10=10^{6-1}=10^5\)
\(\cdot5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^4=5^4\)
\(\cdot4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^6=4^3\)
\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^5\)
\(18^3:9^3=\left(18:9\right)^3=2^3\)
a, 325 . 2566 . 102410 = (25)5 . (28)6 . (210)10 = 225 . 248 . 2100 = 225 + 48 + 100 = 2173
b,279 . 2437 . 72912 = (33)9 . (35)7 . (36)12 = 327 . 335 . 372 = 327 + 35 + 72 = 3134
c,1213 . 189 . 2425 = (3 . 22)13 . (32 . 2)9 . (23 . 3)25 = 313 . 226 . 318 . 29 . 275 . 325 = 313 + 18 + 25 . 226 + 9 + 75 = 356 . 2110
d,1089 . 366 . 7217 = (33 . 22)9 . (32 . 22)6 . (23 . 32)17 = 327 . 218 . 312 . 212 . 251 . 334 = 327 + 12 + 34 . 218 + 12 + 51 = 373 . 281
(27.26.625):(53.64.32)
=(33.26.54):(53.26.32)
=3.5=15
\(\frac{27.2^{10}.3^9.32}{6^{12}}\)
\(=\frac{3^3.2^{10}.3^9.2^5}{\left(2.3\right)^{12}}\)
\(=\frac{3^{12}.2^{15}}{2^{12}.3^{12}}=2^3=8\)