$a)357\cdot {10}^4=3,57\cdot 100\cdot {10}^4=3,57\cdot {10}^2\cdot {10}^4=3,57\cdot {10}^{2+4}=3,57\cdot {10}^6$  

$b)25,3\cdot {10}^5=2,53\cdot 10\cdot {10}^5=2,53\cdot {10}^{1+5}=2,53\cdot {10}^6$  

$c)0,013\cdot {10}^{15}=1,3:100\cdot {10}^{15}=1,3\cdot {10}^{15}:100=1,3\cdot {10}^{15}:{10}^2=1,3\cdot {10}^{15-2}=1,3\cdot {10}^{13}$   [I sposób]

$0,013\cdot {10}^{15}=1,3\cdot 0,01\cdot {10}^{15}=1,3\cdot {10}^{-2}\cdot {10}^{15}=1,3\cdot {10}^{-2+15}=1,3\cdot {10}^{13}$   [II sposób]

$d)27,5\cdot {10}^{-3}=2,75\cdot 10\cdot {10}^{-3}=2,75\cdot {10}^{1+\left(-3\right)}=2,75\cdot {10}^{1-3}=2,75\cdot {10}^{-2}$  

$e)5,2\cdot {10}^{20}\cdot 3,5\cdot {10}^{10}=5,2\cdot 3,5\cdot {10}^{20+10}=18,2\cdot {10}^{30}=1,82\cdot 10\cdot {10}^{30}=1,82\cdot {10}^{1+30}=1,82\cdot {10}^{31}$   

$f)\frac{1,25\cdot {10}^{18}}{25\cdot {10}^{12}}=\frac{1,25}{25}\cdot \frac{{10}^{18}}{{10}^{12}}=\left(\frac{125}{2500}\right)\cdot {10}^{18-12}=\frac{5}{100}\cdot {10}^6=5\cdot \frac{1}{100}\cdot {10}^6=5\cdot {10}^{-2}\cdot {10}^6=5\cdot {10}^{-2+6}=5\cdot {10}^4$