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a) \({2^m}{.2^n}=\underbrace {2.2 \ldots .2}_{m{\rm{ }}}{\rm{ }}.\underbrace {2.2 \ldots .2}_{n{\rm{ }}}{\rm{ }}\) = 2m+n
b) \({3^m}:{3^n}=(\underbrace {3.3 \ldots .3}_{m{\rm{ }}}{\rm{ }}):(\underbrace {3.3 \ldots .3}_{n{\rm{ }}}{\rm{ }})\) = 3m-n với \(m \ge n\)
a) \(3^3 : 3^2\)=\(3^{3-2}=3^1\)
b) \(5^{4} : 5^{2}\)=\(5^{4-2}=5^2\)
c) \(8^{3} . 8^{2}\)=\(8^{3+2}=8^5\)
d) Cách 1:
\(5^{4} . 5^{3}: 5^{2}=5^{4+3}:5^2=5^7:5^2=5^{7-2}=5^5\)
Cách 2:
\(5^{4} . 5^{3}: 5^{2}=5^{4+3-2}=5^5\)
a. \(3^4.3^5=3^9\)
\(16.2^9=2^4.2^9=2^{13}\)
\(16.32=2^4.2^5=2^9\)
b. \(12^8.12=12^9\)
\(243:3^4=3^5:3^4=3\)
\(10^9:10000=10^9:10^4=10^5\)
c. \(4.8^6.2.8^3=2^2.2^{18}.2.2^9=2^{30}\)
\(12^2.2.12^3.6=12^2.12.12^3=12^6\)
\(6^3.2.6^4.3=6^3.6.6^4=6^8\)
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) 53.57 = 53+7 = 510
b) 24.25.29=24+5+9 = 218
c) 102.104.106.108 = 102+4+6+8 = 1020.
a) \(\frac{6}{5}.{\left( {1,2} \right)^8} = 1,2.{(1,2)^8} = {(1,2)^{1 + 8}} = {(1,2)^9}\)
b) \({\left( {\frac{{ - 4}}{9}} \right)^7}:\frac{{16}}{{81}} = {\left( {\frac{{ - 4}}{9}} \right)^7}:{\left( {\frac{{ - 4}}{9}} \right)^2} = {\left( {\frac{{ - 4}}{9}} \right)^{7 - 2}} = {\left( {\frac{{ - 4}}{9}} \right)^5}\)
a) 3 2
b) 3 2
c) 3 1
d) 5 2
e) 10 3
f) 12 0