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

\(12^2.3.12^3.4=\left(4.3\right)^2.3.4=4^2.3^2.3.4=3^3.4^3=27.64=1728\)

\(12^2.3.12^3.4=12^5.3.4=\left(3.4\right)^5.3.4=3^5.4^5.3.4=3^6.4^6=729.4096=\text{2985984}\)

\(3^6.4^6\)

a)\({\left[ {{{\left( { - \frac{1}{6}} \right)}^3}} \right]^4}\) (với \(a =  - \frac{1}{6}\))

\(=(- \frac{1}{6})^{3. 4}=(- \frac{1}{6})^{12}\)

b)\({\left[ {{{\left( { - 0,2} \right)}^4}} \right]^5}\) (với \(a =  - 0,2\))

\(=(-0,2)^{4.5}=(-0,2)^{20}\)

a)

\(\begin{array}{l}{11^7}{.11^3} =11^{7-3}={11^4};\,\,\,\,\,\,\,{11^7}:{11^7} =11^{7-7}=11^0= 1;\\{7^2}{.7^4} = 7^{2+4}= {7^6};\,\,\,\,\,\,\,\,\,\,\,\,\,{7^2}{.7^4}:{7^3} = 7^{2+4-3}= {7^3}.\end{array}\)

b) +) Phép tính đúng là:

\({9^7}:{9^2} = {9^5}\) vì \({9^7}:{9^2}=9^{7-2} = {9^5}\)

+) Các phép tính sai là:

\({2^{11}}:{2^8} = 6 \) vì \({2^{11}}:{2^8} = 2^{11-8} = 2^3\) ;

\({7^{10}}:{7^2} = {7^5}\) vì \({7^{10}}:{7^2} = 7^{10-2} = 7^8\);

\({5^6}:{5^6} = 5\) vì \({5^6}:{5^6}=5^{6-6}=5^0 =1\)

6 mũ 5 nha bạn

\(3^3.3^4=2187\)

\(5^2.5^7=1953125\)

\(7^{5.7}=7^{35}\)

3^3.3^4=3^7=2187

5^2.5^7=5^9=1953125

7^5.7=7^6=117649

bn k mik nhoa!

\(3^3.3^4=3^7\)

\(5^2.5^7=5^9\)

\(7^{5.7}=7^{35}\)

a: =2022^5

b: =3*2*3*2*3^2*2^2

=3^4*2^4

=6^4

\(a,2022^8:2022^3=2022^{8-3}=2022^5\\ b,-6.6.6.3.2.2.\left(-3\right)=6.6.6.3.2.2.3=6.6.6.6.6=6^5\)