1) \(9\cdot9\cdot9\cdot9\cdot3\cdot3\)

\(=3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\)

\(=3^{10}\)

2) \(8\cdot2\cdot2\cdot2\cdot16\cdot4\)

\(=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\)

\(=2^{12}\)

3) \(3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5\cdot5\)

\(=3^4\cdot5^4\)

4) \(25\cdot25\cdot25\cdot5\)

\(=5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\)

\(=5^7\)

5) \(7\cdot49\cdot7\cdot7\cdot7\)

\(=7\cdot7\cdot7\cdot7\cdot7\cdot7\)

\(=7^6\)

6) \(8\cdot64\cdot8\cdot64\)

\(=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\)

\(=2^{18}\)

7) \(2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot4\)

\(=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\)

\(=2^8\)

1) 3¹⁰

2) 2¹²

3)3⁴ . 5⁴

4) 5⁷

5) 7⁶

6)8⁶

7) 2⁸.

Lời giải:

$=\sqrt{4^2}.\sqrt{5^2}+\sqrt{14^2}: \sqrt{7^2}$

$=4.5+14:7=20+2=22$

400+4 =404

\(\left(2x-5\right)^2=\left(x-\dfrac{5}{2}\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}2x-5=x-\dfrac{5}{2}\\2x-5=\dfrac{5}{2}-x\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\3x=\dfrac{15}{2}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\\ \Leftrightarrow x=\dfrac{5}{2}\)

Vậy x = \(\dfrac{5}{2}\)

\(\left(2x-5\right)^2=\left(x-\dfrac{5}{2}\right)^2\)

\(\Leftrightarrow2x-5=x-\dfrac{5}{2}\)

\(\Leftrightarrow2x-x=-\dfrac{5}{2}+5\)

\(\Leftrightarrow x=\dfrac{5}{2}\)

\(...\Rightarrow\dfrac{20\left(x+2\right)}{360}+\dfrac{45\left(x+4\right)}{360}+\dfrac{72\left(x+5\right)}{360}=\dfrac{360\left(x+14\right)}{360}\)

\(\Rightarrow20\left(x+2\right)+45\left(x+4\right)+72\left(x+5\right)=360\left(x+14\right)\)

\(\Rightarrow20x+40+45x+180+72x+360=360x+5040\)

\(\Rightarrow137x+580=360x+5040\)

\(\Rightarrow360x-137x=5040-580\)

\(\Rightarrow223x=4460\Rightarrow x=4460:223=\dfrac{4460}{223}\)

\(2\times3\times5+25\times8\times4+70+4\times2\times25\)

\(=15\times2+100\times8+70+100\times2\)

\(=30+800+70+200\)

\(=\left(30+70\right)+\left(800+200\right)\)

\(=100+100\times10\)

\(=100+1000\)

\(=1100\)

a) \(9^3\cdot3^2\)

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

\(=3^6\cdot3^2\)

\(=3^8\)

b) \(x^7\cdot x:x^4\)

\(=x^8:x^4\)

\(=x^4\)

c) \(7\cdot3^9+3^{10}+51\cdot3^8\)

\(=3^8\cdot\left(7\cdot3+3^2+51\right)\)

\(=3^8\cdot81\)

\(=3^8\cdot3^4\)

\(=3^{12}\)

d) \(5^{15}\cdot125^3\cdot625\)

\(=5^{15}\cdot5^9\cdot5^4\)

\(=5^{28}\)

7h 32 phút nhé

8 giờ 56 phút - 1 giờ 24 phút = 7 giờ 32 phút 

\(n.\left(n+1\right):2=210\Rightarrow n.\left(n+1\right)=210.2=420\)

Ta thấy \(20x21=420\)

\(\Rightarrow n=20\)

\(\left(-\dfrac{1}{2}\right)^5=-\left(\dfrac{1}{2}\right)^5=-\dfrac{1}{32}\)

\(\left(-\dfrac{2}{3}\right)^4=\left(\dfrac{2}{3}\right)^4=\dfrac{2^3}{3^4}=\dfrac{8}{81}\)