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: \(8=2^3\)

\(125=5^3\)

\(27=3^3\)

\(64=8^2\)

\(81=9^2\)

\(1000=10^3\)

\(10000000=10^7\)

1000..000=10^k

b: \(7\cdot7\cdot7=7^3\)

\(7\cdot8\cdot7\cdot25=7^2\cdot200=70^2\cdot2^2\)

a) \(2^3;5^3;3^3;4^3;3^4;5^4;10^3;10^7;10^k3^4\)

a)3^3-2=3

b)625/25=25=5^2

c)8^3+2=8^5

d)5^4+3/5^2=5^7:5^2=5^7-2=5^5

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)  \(\frac{6}{5}.{\left( {1,2} \right)^8} = 1,2.{(1,2)^8} = {(1,2)^{1 + 8}} = {(1,2)^9}\)

b) \({\left( {\frac{{ - 4}}{9}} \right)^7}:\frac{{16}}{{81}} = {\left( {\frac{{ - 4}}{9}} \right)^7}:{\left( {\frac{{ - 4}}{9}} \right)^2} = {\left( {\frac{{ - 4}}{9}} \right)^{7 - 2}} = {\left( {\frac{{ - 4}}{9}} \right)^5}\)

\(2^3.2^2.8^3\)

\(=2^3.2^2.\left(2^3\right)^3\)

\(=2^3.2^2.2^9\)

\(=2^{3+2+9}=2^{14}\)

\(2^3.2^2.8^3\)

\(=2^{3+2}.8^3\)

\(=2^5.8^3\)

\(=2^5.2^9\)

\(=2^{5+9}\)

\(=2^{14}\)

\(a.\) \(5\cdot5\cdot5\cdot5=5^4\)

\(b.\) \(9\cdot9\cdot9\cdot9\cdot9\cdot9\cdot9=9^7\)

\(c.\) \(7\cdot7\cdot7\cdot7\cdot7=7^5\)

\(d.\) \(a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a=a^8\)

5.5.5.5 ta đc 5⁴

9.9.9.9.9.9.9 ta đc 9⁷

7.7.7.7.7 ta đc 7⁵

a.a.a.a.a.a.a.a ta đc a⁸

\(4^2\times8^2\)

\(=\left(2^2\right)^2\times\left(2^3\right)^2\)

\(=2^4\times2^6=2^{10}\)

4²x8²=(4x8)²

         =32²

a) \(2^{36}\)

b) \(3^{30}\)

c) \(3^9\)

d) \(2^{18}\)

a) 4⁸.2²⁰=(2²)⁸.2²⁰=2¹⁶.2²⁰=2³⁶

b) 9¹².27²=(3²)¹².(3³)²=3²⁴.3⁶=3³⁰

c) 3⁶.3².3=3⁹

d) 4⁵.16²=(2²)⁵.(2⁴)²=2¹⁰.2⁸=2¹⁸