$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a) 7.7.7.7=7^{4}\\ b) x.x.x.x.x=x^{5}\\ c) \ 15.5.15.3=15^{2} .15=15^{3}\\ d) 10.10.10=10^{3}\\ e) 3a.3a.3a.3a=( 3a)^{4}\\ g) a^{2} .a=a^{3}\\ b) 11^{7} .11.11^{3} =11^{11}\\ i) \ x^{15} :x^{2} =x^{15-2} =x^{13}\\ k) 20^{30} :2=20^{30-1} =20^{29}\\ m) 5.5^{2} .5^{9} =5^{1+2+9} =5^{12}\\ Bài\ 2:\\ a) \ 2^{3} =8\\ b) 2^{4} =16\\ c) 2^{5} =32\\ d) 2^{10} =1024\\ e) 3^{5} =243\\ g) 5^{3} =125;5^{4} =625;5^{5} =3125\\ h) 3^{4} =81;4^{3} =64;4^{5} =1024\\ k) \ mũ\ không\ là\ =1\ \\ i) \ mũ\ 1\ bằng\ chính\ số\ đó\ \\ Bài\ 3:\ Các\ số\ chính\ phương\ là\ :1;81;16;144;625\\ Vì\ :1^{2} =1;9^{2} =81;4^{2} =16;12^{2} =144;25^{2} =625\\ Bài\ 4:\\ a) 4.16=4.4^{2} =4^{3}\\ b) 13^{2} -12^{2} =25=5^{2}\\ c) 1^{3} +2^{3} +3^{3} +4^{3} +5^{3}\\ =1^{2} .1+2^{2} .2+3^{2} .3+4^{2} .4+5^{2} .5\\ =1+4( 2+16) +27+125\\ =1+72+27+125=225=15^{2}\\ Bài\ 5:\ \\ a) 2^{x} =64\\ 2^{x} =2^{6}\\ \rightarrow x=6\\ b) 2^{x-3} =32\\ \rightarrow 2^{x-3} =2^{5}\\ \rightarrow x-3=5\ \\ \rightarrow x=8\\ c) 3^{x+1} =243\\ 3^{x+1} =3^{5}\\ \rightarrow x+1=5\\ \rightarrow x=4\\ d) \ 2^{x} +12=44\\ \rightarrow 2^{x} =32\\ \rightarrow 2^{x} =2^{5}\\ \rightarrow x=5\\ e) 2^{2x-1} =128\\ \rightarrow 2^{2x-1} =2^{7}\\ \rightarrow 2x-1=7\\ \rightarrow x=4\\ h) 2^{x} .4=64\\ \rightarrow 2^{2x} =2^{6}\\ -2x=6\\ \rightarrow x=3\\ i) 3^{2} .3^{x} =81\\ 3^{2x} =2^{4}\\ \rightarrow 2x=4\\ \rightarrow x=2\\ k) \ 2^{5} .2^{x-1} =1024\\ 2^{5x-5} =2^{10}\\ \rightarrow 5x-5=10\\ \rightarrow x=3\\ m) 5^{2} .5^{x-3} =625\\ \rightarrow 5^{2x-6} =5^{4}\\ \rightarrow 2x-6=4\\ \rightarrow x=5\\ \\ \end{array}$