$a)$  

$2^4=2\cdot 2\cdot 2\cdot 2=16$  

 

${128}^0=1\text{, bo }{a}^0=1\text{, gdzie }a\text{ jest dowolną liczbą}$  

 

${\left(-5\right)}^3=\left(-5\right)\cdot \left(-5\right)\cdot \left(-5\right)=-125$  

 

$0^{15}=\underset{15\text{razy liczba }0}{\underbrace{0\cdot 0\cdot 0\cdot \dots \cdot 0}}=0$  

${\left(-1\right)}^{317}=\underset{317\text{ razy liczba }0}{\underbrace{\left(-1\right)\cdot \left(-1\right)\cdot \dots \cdot \left(-1\right)}}=-1\text{, poniewaz˙ }317\text{ jest liczbą nieparzystą}$  

 

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$b)$  

${\left(-\frac{1}{2}\right)}^5=\left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)\cdot \left(-\frac{1}{2}\right)=-\frac{1}{2\cdot 2\cdot 2\cdot 2\cdot 2}=-\frac{1}{32}$  

 

${\left(\frac{2}{3}\right)}^4=\frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}=\frac{2\cdot 2\cdot 2\cdot 2}{3\cdot 3\cdot 3\cdot 3}=\frac{16}{81}$  

 

${\left(-\frac{1}{4}\right)}^3=\frac{{\left(-1\right)}^3}{{\left(4\right)}^3}=-\frac{1}{64}$  

 

${\left(-\frac{1}{7}\right)}^2=\frac{{\left(-1\right)}^2}{7^2}=\frac{1}{49}$  

 

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$c)$  

${\left(1\frac{1}{4}\right)}^2={\left(\frac{5}{4}\right)}^2=\frac{5^2}{4^2}=\frac{25}{16}=1\frac{9}{16}$  

 

${\left(-0,02\right)}^5=\left(-0,02\right)\cdot \left(-0,02\right)\cdot \left(-0,02\right)\cdot \left(-0,02\right)\cdot \left(-0,02\right)=0,0000000032$  

 

${\left(-1,1\right)}^2=\left(-1,1\right)\cdot \left(-1,1\right)=1,21$  

 

${\left(-2\frac{1}{3}\right)}^3={\left(-\frac{7}{3}\right)}^3=\frac{{\left(-7\right)}^2}{3^3}=\frac{\left(-7\right)\cdot \left(-7\right)\cdot \left(-7\right)}{3\cdot 3\cdot 3}=-\frac{343}{27}=-\frac{324+19}{27}=-12\frac{19}{27}$