\(A=4^2\cdot6^3\)

\(A=\left(2^2\right)^2\cdot3^3\cdot2^3\)

\(A=2^4\cdot2^3\cdot3^3\)

\(A=2^{4+3}\cdot3^3\)

\(A=2^7\cdot3^3\)

\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)

Đặt \(\left(1\right)=A\)

\(\Rightarrow A=1+5^2+...+5^{2x}\)

\(\Rightarrow5^2A=5^2+5^4+...+5^{2x+2}\)

\(\Rightarrow25A=5^2+5^4+...+5^{2x+2}\)

\(\Rightarrow25A-A=5^2+5^4+...+5^{2x+2}-1-5^2-...-5^{2x}\)

\(\Rightarrow24A=5^{2x+2}-1\)

\(\Rightarrow A=\dfrac{5^{2x+2}-1}{24}\)

Mà: \(A=\dfrac{25^6-1}{24}\)

\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)

\(\Rightarrow5^{2x+2}-1=5^{12}-1\)

\(\Rightarrow5^{2x+2}=5^{12}\)

\(\Rightarrow2x+2=12\)

\(\Rightarrow2x=10\)

\(\Rightarrow x=\dfrac{10}{2}\)

\(\Rightarrow x=5\)

\(3^{x-1}+3^x+3^{x+1}=39\)

\(3^{x-1}+3^{x-1}.3+9.3^{x-1}=39\)

\(13.3^{x-1}=39\)

\(3^{x-1}=39:13=3\)

\(x-1=1\)

\(x=2\)

Sửa đề: 3ˣ⁻¹ + 3ˣ + 3ˣ⁺¹ = 39

3ˣ⁻¹ + 3ˣ + 3ˣ⁺¹ = 39

3ˣ⁻¹.(1 + 3 + 3²) = 39

3ˣ⁻¹ . 13 = 39

3ˣ⁻¹ = 39 : 13

3ˣ⁻¹ = 3

x - 1 = 1

x = 1 + 1

x = 2

\(87-\left(73-x\right)=20\)

\(73-x=87-20\)

\(73-x=67\)

\(x=73-67\)

\(x=6\)

\(87-\left(73-x\right)=20\\ \Rightarrow73-x=67\\ \Rightarrow x=6.\)

Bài 1: Bạn xem lại đã viết đúng đề chưa vậy.

Bài 2:

$P=29-|16+3.2|+1=29-|22|+1=29-22+1=7+1=8$

\(3^2.5+2^3.10-3^4:3\)

\(=5\left(3^2+2^3.2\right)-3^{4-1}\)

\(=5\left(9+16\right)-3^3\)

\(=5.25-27\)

\(=125-27=98\)

\(3^2\times5+2^3\times10-3^4:3\\ =9\times5+8\times10-27\\ =45+80-27\\ =98.\)

\(D=-\dfrac{4}{5}+\dfrac{4}{5^2}-\dfrac{4}{5^3}+...+\dfrac{4}{5^{200}}\)

\(\Rightarrow D=4\left(-\dfrac{1}{5}+\dfrac{1}{5^2}-\dfrac{1}{5^3}+...+\dfrac{1}{5^{200}}\right)\)

\(5D=4\cdot\left(-1+\dfrac{1}{5}-\dfrac{1}{5^2}+...+\dfrac{1}{5^{199}}\right)\)

\(\Rightarrow5D+D=4\cdot\left(-1+\dfrac{1}{5}-\dfrac{1}{5^2}+...+\dfrac{1}{5^{199}}-\dfrac{1}{5}+\dfrac{1}{5^2}-\dfrac{1}{5^3}+...+\dfrac{1}{5^{200}}\right)\)

\(\Rightarrow6D=4\cdot\left(\dfrac{1}{5^{200}}-1\right)\)

\(\Rightarrow D=\dfrac{2}{3}\cdot\left(\dfrac{1}{5^{200}}-1\right)\)

oki

(x + 1)³ - 4 = 60

(x + 1)³ = 60 + 4

(x + 1)³ = 64

(x + 1)³ = 4³

x + 1 = 4

x = 4 - 1

x = 3

\(B=7-7^4+7^7-7^{10}+...+7^{295}-7^{298}+7^{301}\)

\(=7\left(1-7^3\right)+7^7\left(1-7^3\right)+...+7^{295}\left(1-7^3\right)+7^{301}\)

\(=\left(1-7^3\right)\left(7+7^7+...+7^{295}\right)+7^{301}\)

\(=\left(1-7^3\right)\left(\dfrac{7^{296}-7}{6}\right)+7^{301}\)

\(=-57\left(7^{296}-7\right)+7^{301}\)