ta có công thức như sau :

\(a^{-x}=?\)

lời giải công thức này như sau :

\(a^{-x}=\left(\frac{1}{a}\right)^x\)

vậy bài cũng gải tương tự 

\(32^{-x}.16^x=\left(\frac{1}{32}\right)^x.\left(16^x\right)\)

\(=\left(\frac{16}{32}\right)^x=\left(\frac{1}{2}\right)^x=2^{-x}\)

mà \(2048=2^{11}\)

 \(\Rightarrow-x=11\)

 \(\Leftrightarrow x=-11\)

vậy \(x=-11\)

\(\Rightarrow\)\(\left(\frac{1}{32}\right)^x\cdot16^x=2048\)

\(\Rightarrow\)\(\left(\frac{1}{2}\right)^x=\left(\frac{1}{2}\right)^{-11}\)

\(\Rightarrow\)\(x=-11\)

a) \(\dfrac{1}{9}.27^n=3^n\)

\(\Leftrightarrow\dfrac{1}{9}=3^n:27^n\)

\(\Leftrightarrow\dfrac{1}{9}=\left(\dfrac{3}{27}\right)^n\)

\(\Leftrightarrow\dfrac{1}{9}=\left(\dfrac{1}{9}\right)^n\)

\(\Leftrightarrow n=1\)

b) \(3^{-2}.3^4.3^n=3^7\)

\(\Leftrightarrow3^2.3^n=3^7\)

\(\Leftrightarrow3^n=3^7:3^2\)

\(\Leftrightarrow3^n=3^5\)

\(\Leftrightarrow n=5\)

c) \(32^{-n}.16^n=2048\)

\(\Leftrightarrow\left(2^5\right)^{-n}.\left(2^4\right)^n=2^{11}\)

\(\Leftrightarrow2^{-5n}.2^{4n}=2^{11}\)

\(\Leftrightarrow2^{-n}=2^{11}\)

\(\Leftrightarrow n=-11\)

a)\(32^{-n}\cdot16^n=2048\)

\(\left(2^5\right)^{-n}\cdot\left(2^4\right)^n\)=2048

\(2^{-5n}\cdot2^{4n}\)=\(2^{11}\)

\(2^{-5n+4n}=2^{11}\)

\(2^{-x}=2^{11}\)

\(\Rightarrow x=-11\)

b)\(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)

\(\frac{1}{2}\cdot2^n+4\cdot2^n=288\)

\(2^n\left(\frac{1}{2}+4\right)=288\)

\(2^n\cdot\frac{9}{2}=288\)

\(2^n=288:\frac{9}{2}\)

\(2^n=64\)

\(2^n=2^6\)

\(\Rightarrow n=6\)

a) 32^-n . 16ⁿ = 2048

\(\frac{1}{32n}\) . 16ⁿ = 2048

\(\frac{1}{2^n.16^n}\) . 16ⁿ = 2048

\(\frac{1}{2^n}\) = 2048

2^-n = 2048

2^-n = 2¹¹

\(\Rightarrow\) -n = 11

\(\Rightarrow\) n = -11

Vậy n = -11

C1) 1357 x 2048 + 357 x 2048 = 2779136 + 731136 = 3510272

C2) 1357 x 2048 + 357 x 2048 = 2048 x (1357 + 357) = 3510272

C3) 1357 x 2048 + 357 x 2048

= 1357 x 2048 + (1357 - 1000) x 2048

= 1357 x 2048 + 1357 x 2048 -1000 x 2048

= 2048 x (1357 + 1357 - 1000)

= 2048 x 1714

= 3510272

:) 1357 x 2048 + 357 x 2048

= 1357 x 2048 + (1357 - 1000) x 2048

= 1357 x 2048 + 1357 x 2048 -1000 x 2048

= 2048 x (1357 + 1357 - 1000)

= 2048 x 1714

= 3510272

\(C1:1357\cdot2048+357\cdot2048\)

\(=2779136+731136\)

\(=3510272\)

\(C2:2048\cdot\left(1357+357\right)\)

\(2048\cdot1714\)

\(=3510272\)

\(C3:\left(1000+357\right)\cdot2048+357\cdot2048\)

\(1000\cdot2048+357\cdot2048+357\cdot2048\)

\(2048000+2\cdot\left(357\cdot2048\right)\)

\(2048000+1462272\)

\(3510272\)