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a) 76:74 = 76−4 = 72
b) 1091100: 1091100 = 1091100−100 = 10910
a) 53.57 = 53+7 = 510
b) 24.25.29=24+5+9 = 218
c) 102.104.106.108 = 102+4+6+8 = 1020.
a: \(8=2^3\)
\(125=5^3\)
\(27=3^3\)
\(64=8^2\)
\(81=9^2\)
\(1000=10^3\)
\(10000000=10^7\)
1000..000=10k
b: \(7\cdot7\cdot7=7^3\)
\(7\cdot8\cdot7\cdot25=7^2\cdot200=70^2\cdot2^2\)
\(a,125^5:25^3=\left(5^3\right)^5:\left(5^2\right)^3=5^{15-6}=5^9\)
\(b,27^6:9^3=\left(3^3\right)^6:\left(3^2\right)^3=3^{18-6}=3^{12}\)
\(c,4^{20}:2^{15}=\left(2^2\right)^{20}:2^{15}=2^{40-15}=2^{25}\)
\(d,24^n:2^{2n}=4^n.6^n:4^n=6^n\)
\(e,64^4.16^5:4^{20}=\left(2^6\right)^4.\left(2^4\right)^5:\left(2^2\right)^{20}=2^{24+20-40}=2^4=16\)
a: \(4^5\cdot8^7=2^{10}\cdot2^{21}=2^{31}\)
b: \(125^5\cdot25^3=5^{15}\cdot5^6=5^{21}\)
a) `7^4 .7^5 .7^6 = 7^(4+5+6)=7^(15)`
b) `(54:3^7) .324 =( 2.3^3 : 3^7).2^2 x3^4`
`=(2: 3^4).3^4 .2^2`
`= 2.2^2=2^3`
c) `[(8+2^2).10^100] : (10^0 .10^94)`
`=(12 . 10^100) : 10^94`
`=12 . (10^100 : 10^94)`
`=12 . 10^6`
d) `a^9 :a^9 = a^(9-9)=a^0`
a) 1024 : 26
= 210 : 26
= 210 - 6 = 24
b) 37 : 27
= 37 : 33
= 37 - 3 = 34