\(A=1+2+2^2+2^3+....+2^{30}\)

\(2.A=2+2^2+2^3+2^4+...+2^{30}\)

\(2.A-A=\left(2+2^2+2^3+2^4+...+2^{31}\right)-\left(1+2+2^2+2^3+...+2^{30}\right)\)

\(A=2^{31}-1\)

\(\Rightarrow A+1=2^{31}-1+1\)

\(\Rightarrow A+1=2^{31}\)

2 mũ 31

\(A=1+3+3^2+...+3^{41}\)

\(3A=3+3^2+3^3+...+3^{42}\)

\(3A-A=3+3^2+...+3^{42}-1-3-...-3^{41}\)

\(2A=3^{42}-1\)

\(A=\dfrac{3^{42}-1}{2}\)

Ta có: \(2A+1\)

\(=2\cdot\dfrac{3^{42}-1}{2}+1\)

\(=3^{42}-1+1\)

\(=3^{42}\)

\(=\left(3^2\right)^{21}\)

\(=9^{21}\)

a: $2^6\cdot 3^3={\left(2^2\cdot 3\right)}^3={12}^3$

b: $6^4\cdot 8^3=2^4\cdot 3^4\cdot 2^9=2^{13}\cdot 3^4$

c: $16\cdot 81={36}^2$

d: ${25}^4\cdot 2^8={100}^4$

\(A=1+2+2^2+...+2^{30}\)

\(2A=2+2^2+2^3+...+2^{31}\)

\(2A-A=\left(2+2^2+2^3+...+2^{31}\right)-\left(1+2+2^2+...+2^{30}\right)\)

\(A=2^{31}-1\)

\(A+1=2^{31}\)

A=1+2+2²+.....+2³⁰                                                                                           2A=2+2²+2³+......+2³¹                                                                                     2A=

\(2^3x2^2x2^4=2^9\)nha bạn

2³

2²

2⁴

xong rồi đó bạn nhớ kb với mk nha!

a² = a.a

a³ = a.a.a

aⁿ = a.a.a.............a

a: \(A=8^2\cdot32^4=2^6\cdot2^{20}=2^{26}\)

b: \(B=27^3\cdot9^4\cdot243=3^9\cdot3^8\cdot3^5=3^{22}\)

\(2^3\cdot2^2\cdot2^x\cdot x^5\cdot=2^{5+x}\cdot x^5\)

\(10^2\cdot2^{10}\cdot10^3\cdot10^5=10^{10}\cdot2^{10}=2^{10}\cdot5^{10}\cdot2^{10}=4^{10}\cdot5^{10}=20^{10}\)

\(a^3\cdot a^2\cdot a^5=a^{3+2+5}=a^{10}\)

P/s: Mình chỉ hiểu ý bạn như này!

 trả lời ngu như mày

\(16^2:4^2\)

\(=\left(4^2\right)^2:4^2\)

\(=4^4:4^2\)

\(=4^{4-2}\)

\(=4^2\)

==========

\(25^5:5^2\)

\(=\left(5^2\right)^5:5^2\)

\(=5^{10}:5^2\)

\(=5^{10-2}\)

\(=5^8\)

============

\(9^8:3^2\)

\(=\left(3^2\right)^8:3^2\)

\(=3^{16}:3^2\)

\(=3^{16-2}\)

\(=3^{14}\)

===========

\(a^6:a\)

\(=a^{6-1}\)

\(=a^5\)