a) 3.3^4.3^5 = 3^10

b) 7^3 : 7^2 : 7 = 7^1

c) (x^4)^3 = x^12

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: 

\(5^{4} . 5^{3}: 5^{2}=5^{4+3-2}=5^5\)

MIK SỬA LẠI ĐỀ CÂU B

a) \(27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)

b) \(3^9:81^3=3^9:\left(3^4\right)^3=3^9:3^{12}=3^{-3}\)

a) \(\left(3^3\right)^5:\left(3^4\right)^3\)

= \(3^{15}:3^{12}\)

= \(3^3\)

a) \(27^5:81^3=3^{15}:3^{12}=3^3\)

b) \(3^9:81^3=3^9:3^{12}=\dfrac{1}{3^3}=\left(\dfrac{1}{3}\right)^3\)

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: =3^4*3^9=3^13

b: =2^10:2^7*2^20*2^30=2^53

c: =2^12*2^10*2^30=2^52

a) \(9^2\cdot27^3\)

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

\(=3^4\cdot3^9\)

\(=3^{4+9}\)

\(=3^{13}\)

b) \(4^5:2^7\cdot4^{10}\cdot2^{30}\)

\(=\left(2^2\right)^5:2^7\cdot\left(2^2\right)^{10}\cdot2^{30}\)

\(=2^{10}:2^7\cdot2^{20}\cdot2^{30}\)

\(=2^3\cdot2^{20}\cdot2^{30}\)

\(=2^{3+20+30}\)

\(=2^{53}\)

c) \(64^2\cdot4^5\cdot2^{30}\)

\(=\left(2^6\right)^2\cdot\left(2^2\right)^5\cdot2^{30}\)

\(=2^{12}\cdot2^{10}\cdot2^{30}\)

\(=2^{12+10+30}\)

\(=2^{52}\)

1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)

b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)

c) \(10^8\div10^3=10^{8-3}=10^5\)

d) \(a^7\div a^2=a^{7-2}=a^5\)

2.

\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)

\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)

\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)

còn bài 2

a) \({2^m}{.2^n}=\underbrace {2.2 \ldots .2}_{m{\rm{ }}}{\rm{ }}.\underbrace {2.2 \ldots .2}_{n{\rm{ }}}{\rm{ }}\) = 2^m+n

b) \({3^m}:{3^n}=(\underbrace {3.3 \ldots .3}_{m{\rm{ }}}{\rm{ }}):(\underbrace {3.3 \ldots .3}_{n{\rm{ }}}{\rm{ }})\) = 3^m-n  với \(m \ge n\)

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. \(4.8^6.2.8^3=2^2.2^{18}.2.2^9=2^{30}\)

\(12^2.2.12^3.6=12^2.12.12^3=12^6\)

\(6^3.2.6^4.3=6^3.6.6^4=6^8\)

he

a. 

16.29=24.29=21316.29=24.29=213

b. 

c. 4.86.2.83=22.218.2.29=2304.86.2.83=22.218.2.29=230

\(a.\) \(5\cdot5\cdot5\cdot5=5^4\)

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

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

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

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

\(\begin{array}{l}{3^3}{.3^4} = {3^{3 + 4}} = {3^7};\\{10^4}{.10^3}  = 10^{4+3}= {10^7};\\{x^2}.{x^5} = x^{2+5} = {x^7}.\end{array}\