$\text{a)}$  

$15\cdot {10}^{-2}=1,5\cdot 10\cdot {10}^{-2}=1,5\cdot {10}^{1+\left(-2\right)}=1,5\cdot {10}^{-1}$  

$n=-1$

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$\text{b)}$  

$2,5\cdot {10}^{-4}\cdot 5,6\cdot {10}^{-2}=\left(2,5\cdot 5,6\right)\cdot {10}^{-4+\left(-2\right)}=14\cdot {10}^{-6}=$

$=1,4\cdot 10\cdot {10}^{-6}=1,4\cdot {10}^{1+\left(-6\right)}=1,4\cdot {10}^{-5}$   

$n=-5$

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$\text{c)}$

$6,2\cdot {10}^{-3}\cdot 1,5\cdot {10}^{-5}:0,3\cdot {10}^n=\left(6,2\cdot 1,5:0,3\right)\cdot {10}^{-3+\left(-5\right)}\cdot {10}^n=$

$=31\cdot {10}^{-8}\cdot {10}^n=3,1\cdot 10\cdot {10}^{-8}\cdot {10}^n=3,1\cdot {10}^{1+\left(-8\right)}\cdot {10}^n=3,1\cdot {10}^{-7}\cdot {10}^n$  

 

${10}^{-7}\cdot {10}^n={10}^{-5}\mid :{10}^{-7}$  

${10}^n={10}^{-5}:{10}^{-7}$  

${10}^n={10}^{-5-\left(-7\right)}$  

${10}^n={10}^{-5+7}$  

${10}^n={10}^2$  

$n=2$