a, (-0,2)² \(\times\) 5 - \(\dfrac{2^{13}\times27^3}{4^6\times9^5}\)

= 0,04 \(\times\) 5 - \(\dfrac{2^{13}\times3^9}{2^{12}\times3^{10}}\)

= 0,2 - \(\dfrac{2}{3}\)

= \(\dfrac{2}{10}\) - \(\dfrac{2}{3}\)

=  - \(\dfrac{7}{15}\)

b, \(\dfrac{5^6+2^2.25^3+2^3.125^2}{26.5^6}\)

 = \(\dfrac{5^6+4.5^6+8.5^6}{26.5^6}\)

= \(\dfrac{5^6.\left(1+4+8\right)}{26.5^6}\)

= \(\dfrac{1}{2}\)

a, (-0,2)2 $\times$ 5 - 213×27346×9546×95213×273​

= 0,04 $\times$ 5 - 213×39212×310212×310213×39​

= 0,2 - 2332​

= 210102​ - 2332​

=  - 715157​

b, 56+22.253+23.125226.5626.5656+22.253+23.1252​

 = 56+4.56+8.5626.5626.5656+4.56+8.56​

= 56.(1+4+8)26.5626.5656.(1+4+8)​

= 1221​
 

1) \(2^x=4^3 \Leftrightarrow2^x=2^6\Leftrightarrow x=6\)

2) \(2^x=4^6\Leftrightarrow2^x=2^{12}\Leftrightarrow x=12\)

3) \(3^x=9^{10}\Leftrightarrow3^x=3^{20}\Leftrightarrow x=20\)

1) 2�=43⇔2�=26⇔�=62x=43⇔2x=26⇔x=6

2) 2�=46⇔2�=212⇔�=122x=46⇔2x=212⇔x=12

3) 3�=910⇔3�=320⇔�=203x=910⇔3x=320⇔x=20

1) 2�=43⇔2�=26⇔�=62x=43⇔2x=26⇔x=6

2) 2�=46⇔2�=212⇔�=122x=46⇔2x=212⇔x=12

3) 3�=910⇔3�=320⇔�=203x=910⇔3x=320⇔x=20

\(A=3+3^2+....+3^{99}\)

\(3A=3^2+3^3+...+3^{100}\)

\(3A-A=3^2+3^3+...+3^{100}-3-3^2-...-3^{99}\)

\(2A=3^{100}-3\)

\(A=\dfrac{3^{100}-3}{2}\)

\(\Rightarrow2A+3=9^{2x+6}\)

\(\Rightarrow2\cdot\dfrac{3^{100}-3}{2}+3=\left(3^2\right)^{2x+6}\)

\(\Rightarrow3^{100}-3+3=3^{2\left(2x+6\right)}\)

\(\Rightarrow3^{100}=3^{4x+12}\)

\(\Rightarrow4x+12=100\)

\(\Rightarrow4x=88\)

\(\Rightarrow x=22\)

`#3107.101107`

\(3^9\div3^8+5^8\div5^7\\ =3^{9-8}+5^{8-7}\\ =3+5\\ =8\)

_______

\(6^9\div6^7-30\\ =6^{9-7}-30\\ =6^2-30\\ =36-30\\ =6\)

________

\(\left(2^7\times2^2\right)\div2^9-5^0\\ =2^{7+2}\div2^9-1\\ =2^9\div2^9-1\\ =2^0-1\\ =1-1\\ =0\)

_______

\(3\times3\times3\times3\times3\times3^5\\ =3^{1+1+1+1+1+5}\\ =3^{10}\)

\(a)\)

\(21\left(x+3\right)^3:\left(3x+9\right)^2\)

\(=[21\left(x+3\right)^3]:[3^2\left(x+3\right)^2]\)

\(=7\left(x+3\right):3\)

Thay vào ta được: \(7.\frac{\left(-6+3\right)}{3}=7.\left(-3\right):3=-7\)

\(b)\)

Thay vào ta được:

\(\left(2.2^2-5.2+3\right)^4:[\left(2.2-3\right)^3:\left(2-1\right)^2]\)

\(=\left(2.4-10+3\right)^4:[\left(4-3\right)^31^2]\)

\(=1^4:\left(1^3.1\right)\)

\(=1:1\)

\(=1\)

\(c)\)

Thay vào ta được:

\(36.10^4.7^3:\left(-6.10^3.7^2\right)\)

\(=-6.10.7\)

\(=-420\)

Bài 9,

6²x73+36x3³=36x73+36x27=36(73+27)=36x100=3600.

197-\([\)6x(5-1)²+2022⁰\(]\):5=197-\([\)6x16+1\(]\):5=197-97:5=197-97/5=888/5.

Bài 10,

21-4x=13

=>4x=21-13=8

=>x=8:4=2.

30:(x-3)+1=4⁵:4³=4²=16

=>30:(x-3)=16-1=15

=>x-3=30:15=2

=>x=2+3=5.

(x-1)³+5x6=38

=>(x-1)³+30=38

=>(x-1)³=38-30=8=2³

=>x-1=2

=>x=3.