$a)$  

Zauważmy, że:

$16:2=8\text{, potem }8:2=4\text{ i }4:2=2$  

Z tego wynika, że:

$16=2\cdot 8=$  

$=2\cdot 2\cdot 4=$

$=2\cdot 2\cdot 2\cdot 2=$   

$=2^4$  

 

$b)$  

$-27:\left(-3\right)=9$  

$9:\left(-3\right)=-3$  

Z tego wynika, że:

$-27=\left(-3\right)\cdot 9=$  

$=\left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)=$  

$={\left(-3\right)}^3$  

 

$c)$  

$3125:5=625$  

$625:5=125$  

$125:5=25$  

$25:5=5$  

Z tego wynika, że:

$3125=5\cdot 625=$  

$=5\cdot 5\cdot 125=$  

$=5\cdot 5\cdot 5\cdot 25=$  

$=5\cdot 5\cdot 5\cdot 5\cdot 5=$  

$=5^5$  

 

$d)$  

$\left(-\frac{1}{32}\right):\left(-\frac{1}{2}\right)=\underset{16}{\begin{array}{c}-\frac{1}{\sout{32}}\end{array}}\cdot \left(-\stackrel{1}{\sout{2}}\right)=\frac{1}{16}$  

$\frac{1}{16}:\left(-\frac{1}{2}\right)=\frac{1}{\underset{8}{\sout{16}}}\cdot \left(-\stackrel{1}{\sout{2}}\right)=-\frac{1}{8}$  

$\left(-\frac{1}{8}\right):\left(-\frac{1}{2}\right)=\underset{4}{\begin{array}{c}-\frac{1}{\sout{8}}\end{array}}\cdot \left(-\stackrel{1}{\sout{2}}\right)=\frac{1}{4}$  

$\frac{1}{4}:\left(-\frac{1}{2}\right)=\frac{1}{4}\cdot \left(-2\right)=-\frac{1}{2}$  

Z tego wynika, że:

$\left(-\frac{1}{32}\right)=\left(-\frac{1}{2}\right)\cdot \frac{1}{16}=$  

$=\left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{8}\right)=$  

$=\left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \frac{1}{4}=$  

$=\left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)=$  

$={\left(-\frac{1}{2}\right)}^5$  

 

$e)$  

$1024:4=256$  

$256:4=64$  

$64:4=16$  

$16:4=4$  

Z tego wynika, że:

$1024=4\cdot 256=$  

$=4\cdot 4\cdot 64=$  

$=4\cdot 4\cdot 4\cdot 16=$  

$=4\cdot 4\cdot 4\cdot 4\cdot 4=$  

$=4^5$  

 

$f)$  

$1024:\left(-2\right)=-512$  

$\left(-512\right):\left(-2\right)=256$  

$256:\left(-2\right)=-128$  

$\left(-128\right):\left(-2\right)=64$  

$64:\left(-2\right)=-32$  

$\left(-32\right):\left(-2\right)=16$  

$16:\left(-2\right)=-8$  

$\left(-8\right):\left(-2\right)=4$  

$4:\left(-2\right)=\left(-2\right)$  

Z tego wynika, że:

$1024=\left(-2\right)\cdot \left(-512\right)=\left(-2\right)\cdot \left(-2\right)\cdot 256=$

$=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-128\right)=$  

$=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot 64=$   

$=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-32\right)=$  

$=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot 16=$  

$=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-8\right)=$  

$=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot 4=$  

$=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)=$  

$={\left(-2\right)}^{10}$  

 

$g)$  

$1296:\left(-6\right)=-216$  

$\left(-216\right):\left(-6\right)=36$  

$36:\left(-6\right)=\left(-6\right)$  

Z tego wynika, że:

$1296=\left(-6\right)\cdot \left(-216\right)=$  

$=\left(-6\right)\cdot \left(-6\right)\cdot 36=$  

$=\left(-6\right)\cdot \left(-6\right)\cdot \left(-6\right)\cdot \left(-6\right)=$  

$={\left(-6\right)}^4$  

 

$h)$  

$\left(-0,000000001\right):\left(-0,1\right)=0,00000001$  

$0,00000001:\left(-0,1\right)=\left(-0,0000001\right)$  

$\left(-0,0000001\right):\left(-0,1\right)=0,000001$  

$0,000001:\left(-0,1\right)=\left(-0,00001\right)$  

$\left(-0,00001\right):\left(-0,1\right)=0,0001$  

$0,0001:\left(-0,1\right)=\left(-0,001\right)$  

$\left(-0,001\right):\left(-0,1\right)=0,01$  

$0,01:\left(-0,1\right)=\left(-0,1\right)$  

Z tego wynika, że:

$\left(-0,000000001\right)=\left(-0,1\right)\cdot 0,00000001=$

$=\left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,0000001\right)=$  

$=\left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot 0,000001=$  

$=\left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,00001\right)=$  

$=\left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot 0,0001=$  

$=\left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,001\right)=$  

$=\left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot 0,01=$  

$=\left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)\cdot \left(-0,1\right)=$  

$={\left(-0,1\right)}^9$