a)4².8²=32²

k giúp

a,=2^72

b,=3^63

c,=7^54

a) \(2^5\cdot2^7\)

\(=2^{5+7}\)

\(=2^{12}\)

b) \(2^3\cdot2^2\)

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

\(=2^5\)

c) \(2^4\cdot2^3\cdot2^5\)

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

\(=2^{12}\)

d) \(2^2\cdot2^4\cdot2^6\cdot2\)

\(=2^{2+4+6+1}\)

\(=2^{13}\)

e) \(2\cdot2^3\cdot2^7\cdot2^4\)

\(=2^{1+3+7+4}\)

\(=2^{15}\)

f) \(3^8\cdot3^7\)

\(=3^{8+7}\)

\(=3^{15}\)

g) \(3^2\cdot3\)

\(=3^{2+1}\)

\(=3^3\)

h) \(3^4\cdot3^2\cdot3\)

\(=3^{4+2+1}\)

\(=3^7\)

I) \(3\cdot3^5\cdot3^4\cdot3^2\)

\(=3^{1+5+4+2}\)

\(=3^{12}\)

Chào bạn, bạn hãy theo dõi lời giải của mình nhé! 

C₁ : Ta có : 

\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)

\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)

\(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)\)

\(A=2-\frac{1}{2^{2012}}=\frac{2^{2013}}{2^{2012}}-\frac{1}{2^{2012}}=\frac{2^{2013}-1}{2^{2012}}\)

C₂ : Ta có : 

\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)

\(\frac{1}{2}A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2013}}\)

\(A-\frac{1}{2}A=\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2013}}\right)\)

\(\frac{1}{2}A=1-\frac{1}{2^{2013}}\)

\(A=\left(1-\frac{1}{2^{2013}}\right).2=1.2-\frac{1}{2^{2013}}.2=2-\frac{1}{2^{2012}}=\frac{2^{2013}}{2^{2012}}-\frac{1}{2^{2012}}=\frac{2^{2013}-1}{2^{2012}}\)

Có gì bạn không hiểu bạn cứ nhắn tin gửi lại mình nhé! Chúc bạn học tốt!

A=﴾ghi lại biieur thức﴿

2A=2+1+1/2+1/2^2+….+1/2^2011

2A‐A=A=﴾2+1+1/2+1/2^2+….+1/2^2011﴿‐﴾1+1/2+1/2^2+...+1/2^2012﴿

A=2‐1/2^201

A=﴾ghi lại biieur thức﴿

2A=2+1+1/2+1/2^2+….+1/2^2011

2A‐A=A=﴾2+1+1/2+1/2^2+….+1/2^2011﴿‐﴾1+1/2+1/2^2+...+1/2^2012﴿

A=2‐1/2^2012

\(3^5:3^3=3^2\)

\(3^8:3^3=3^5\)và \(3^8:3^3=243\)

Ta thấy số mũ của luỹ thừa ta tìm được chính là hiệu của 2 luỹ thừa trên

dự đoán \(\hept{\begin{cases}2^7:2^3=2^4\\2^7:2^4=2^3\end{cases}}\)

- 3^5 / 3^3 = 3^ ( 5 - 3) = 3^ 2 = 9

- 3^8 / 3^3 = 3^ ( 8 - 3) = 3^5 = 243

- 2^7/ 2^3 = 2^ ( 7 - 3) = 2^4 = 16

  2^7/ 2^4 = 2^( 7 - 4) = 2^3 = 8

- 3^5 / 3^3 = 3^ ( 5 - 3) = 3^ 2 = 9

- 3^8 / 3^3 = 3^ ( 8 - 3) = 3^5 = 243

- 2^7/ 2^3 = 2^ ( 7 - 3) = 2^4 = 16

  2^7/ 2^4 = 2^( 7 - 4) = 2^3 = 8

(-7).(-7).(-7).(-7).(-7).(-7) = (-7)6

a)\(\left(\frac{1}{5}\right)^{10}.5^{20}=\left(\frac{1}{5}\right)^{10}.5^{10.2}=\left(\frac{1}{5}\right)^{10}.25^{10}=\left(\frac{1}{5}.5\right)^{10}=1^{10}=1\)

b)\(5^2.3^5.\left(\frac{3}{5}\right)^2=\left(\frac{3}{5}.5\right)^2.3^5=3^2.3^5=3^7\)

c)\(\left(\frac{1}{16}\right)^3:\left(\frac{1}{8}\right)^2=\left(\frac{1}{8}\right)^{2.3}:\left(\frac{1}{8}\right)^2=\left(\frac{1}{8}\right)^{6+2}=\left(\frac{1}{8}\right)^8\)

\(a.\left(\frac{1}{5}\right)^{10}.5^{20}=\left(\frac{1}{5}\right)^{10}.5^{10.2}=\left(\frac{1}{5}\right)^{10}.\left(5^2\right)^{10}=\left(\frac{1}{5}\right)^{10}.25^{10}=\left(\frac{1}{5}.25\right)^{10}=5^{10}.\)

\(b.5^2.3^5.\left(\frac{3}{5}\right)^2=\left[5^2.\left(\frac{3}{5}\right)^2\right].3^5=\left(5.\frac{3}{5}\right)^2.3^5=3^2.3^5=3^7\)\(c.\left(\frac{1}{16}\right)^3:\left(\frac{1}{8}\right)^2=\left[\left(\frac{1}{4}\right)^2\right]^3:\left[\left(\frac{1}{2}\right)^3\right]^2=\left(\frac{1}{4}\right)^6:\left(\frac{1}{2}\right)^6=\left(\frac{1}{4}:\frac{1}{2}\right)^6=\left(\frac{1}{2}\right)^6\)

a-3; b-4; c-2; d-1

Giải thích:

\({3^7}{.3^3}=3^{7+3}=3^{10}\)

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

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

\({5^{12}}{.5^5}=5^{12+5}=5^{17}\)