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\(a,4^9:4^4=4^5\\b,17^8:17^5=17^3\\ c,2^{10}:8^2=2^{10}:2^6=2^4\\ d,18^{10}:3^{10}=2^{10}\cdot3^{20}:3^{10}=2^{10}\cdot3^{10}=6^{10}\\ e,27^5:81^3=3^{15}:3^{12}=3^3 \)
\(f,10^6:100=10^6:10^2=10^4\\ g,5^9:25^3=5^9:5^6=5^3\\ h,4^{10}:64^3=4^{10}:4^9=4\\ i,2^{25}:32^4:18^4:9^4=2^{25}:2^{20}:2^4:3^8:3^8=2\)
a)
49:44=45
178:175=173
210:82=210:24=26
1810:310=1510
275:813=315:312=33
b)106:102=104
59:56=53
410:643=4
225:324=225:220=25
184:94=94
\(4^9:4^4\)
=\(4^{9-4}\)
=\(4^5\)
\(17^8:17^5\)
=\(17^{8-5}\)
= \(17^3\)
\(2^{10}:8^2\)
\(=2^{^{ }10}:\left(2^3\right)^2\)
=\(2^{10}:2^6\)
\(=2^4\)
\(18^{10}:3^{10}\)
=\(\left(18:3\right)^{10}\)
=\(6^{10}\)
a)
49:44=45
178:175=173
210:82=210:24=26
1810:310=1510
275:813=315:312=33
b)106:102=104
59:56=53
410:643=4
225:324=225:220=25
184:94=94
a: \(4^{10}\cdot2^{30}=2^{30}\cdot2^{20}=2^{50}\)
b: \(9^{25}\cdot27^4\cdot81^2=3^{50}\cdot3^{12}\cdot3^8=3^{70}\)
c: \(25^{50}\cdot125^5=5^{100}\cdot5^{15}=5^{115}\)
d: \(64^3\cdot4^8\cdot16^4=4^9\cdot4^8\cdot4^8=4^{25}\)
e: \(2^{10}:8^3=2^{10}:2^9=2\)
\(12^7:6^7=\left(\dfrac{12}{6}\right)^7=2^7\)
f: \(5^8:25^2=5^8:5^4=5^4\)
\(4^9:64^2=4^9:4^6=4^3\)
\(2^{25}:32^4=2^{25}:2^{20}=2^5\)
\(125^3:25^4=5^9:5^8=5\)
g: 2^5*8^4
=2^5*(2^3)^4
=2^5*2^12
=2^17
2:
a: n=5^4
=>n=625
b: n^3=125
=>n^3=5^3
=>n=5
c: 11^n=1331
=>11^n=11^3
=>n=3
a, 4 5 : 4 = 4 4
b, 2 10 : 2 3 = 2 7
c, x 9 : x 3 = x 6 x ≠ 0
d, 5 103 : 5 3 = 5 100
a) \(4^9:4^4\)
\(=4^{9-4}\)
\(=4^5\)
b) \(17^8:17^5\)
\(=17^{8-5}\)
\(=17^3\)
c) \(2^{10}:8^2\)
\(=2^{10}:\left(2^3\right)^2\)
\(=2^{10-6}\)
\(=2^4\)
d) \(18^{10}:3^{10}\)
\(=\left(18:3\right)^{10}\)
\(=6^{10}\)
e) \(27^5:81^3\)
\(=\left(3^3\right)^5:\left(3^4\right)^3\)
\(=3^{15}:3^{12}\)
\(=3^{15-12}\)
\(=3^3\)
f) \(10^6:100\)
\(=10^6:10^2\)
\(=10^{6-2}\)
\(=10^4\)
g) \(5^9:25^3\)
\(=5^9:\left(5^2\right)^3\)
\(=5^9:5^6\)
\(=5^{9-6}\)
\(=5^3\)
h) \(4^{10}:64^3\)
\(=4^{10}:\left(4^3\right)^3\)
\(=4^{10-9}\)
\(=4\)
i) \(2^{25}:32^4:18^4:9^4\)
\(=\left(2^{25}:2^{20}\right):\left(18^4\cdot9^4\right)\)
\(=2^5:9^8:2^4\)
\(=2:9^8\)
\(=\dfrac{2}{9^8}\)
a,4^9-4
b,17^8-5
c,2^10-5
d,6^10
e,81
f,