Bài 1: \(a,7\cdot7\cdot7\cdot7=7^4\\ b,3\cdot5\cdot15\cdot15=3\cdot5\cdot3\cdot5\cdot3\cdot5=\left(3\cdot5\right)^3\\ c,2\cdot2\cdot5\cdot2\cdot5=2^3\cdot5^3\\ d,1000\cdot10\cdot10=10^5\\ e,aaabbb=a^3\cdot b^3\)
Bài 2:
\(a,16\cdot2^{34}=2^4\cdot2^{34}=2^{38}\\ b,a\cdot a^4\cdot a^2=a^7\\ c,a:a^4=a^{-3}=\dfrac{1}{a^3}\\ d,4^{15}:4^5=4^{10}=2^{20}\\ e,4^6:4^6=1\\ g,9^8:3^2=3^{16}:3^2=3^{14}\)
Bài 3:
\(a,3\cdot5^2-16:2^2\\ =3\cdot5^2-16:4\\ =75-4\\ =71\\ b,15\cdot141+59\cdot15\\ =15\cdot\left(141+59\right)\\ =15\cdot200\\ =3000\)
Bài 4:
\(a,3^{75}\cdot27\cdot81^3=3^{75}\cdot3^3\cdot3^{12}=3^{90}\\ b,36^5:18^5=2^5\\ c,24\cdot5^5+5^2\cdot5^3=24\cdot5^5+5^5=25\cdot5^5=5^7\\ d,125^4:5^8=5^{12}:5^8=5^4\)
Bài 5:
\(a,2\cdot4^x=16\\ \Leftrightarrow2^{2x+1}=2^4\\ \Leftrightarrow2x+1=4\\ \Leftrightarrow x=\dfrac{3}{2}\\ b,3\cdot3^x=243\\ \Leftrightarrow3^{x+1}=3^5\\ \Leftrightarrow x+1=5\\ \Leftrightarrow x=4\\ c,64\cdot4^x=16^8\\ \Leftrightarrow4^{x+3}=4^{16}\\ \Leftrightarrow x+3=16\\ \Leftrightarrow x=13\)
