Exemplo 5.1.1. Observe que neste caso o expoente é um número natural, e portanto positivo, como por exemplo:

a)

$2^3=2\cdot 2\cdot 2=8$;

b)

$-2^3=-\left(2\cdot 2\cdot 2\right)=-8$

c)

${\left(-2\right)}^3=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)=-8$;

d)

$2^4=2\cdot 2\cdot 2\cdot 2=16$;

e)

$-2^4=-\left(2\cdot 2\cdot 2\cdot 2\right)=-16$;

f)

${\left(-2\right)}^4=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)=16$;

g)

${\left(\frac{3}{5}\right)}^2=\left(\frac{3}{5}\right)\cdot \left(\frac{3}{5}\right)=\frac{3\cdot 3}{5\cdot 5}=\frac{9}{25}$;

h)

${\left(\frac{-3}{4}\right)}^3=\left(\frac{-3}{4}\right)\cdot \left(\frac{-3}{4}\right)\cdot \left(\frac{-3}{4}\right)=\frac{\left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)}{4\cdot 4\cdot 4}=\frac{-27}{64}$;

i)

${\left(0,02\right)}^4=\left(0,02\right)\cdot \left(0,02\right)\cdot \left(0,02\right)\cdot \left(0,02\right)=\left(0,0004\right)\cdot \left(0,0004\right)=0,00000016$;

j)

${\left(0,02\right)}^4={\left(\frac{2}{100}\right)}^4={\left(\frac{2}{10^2}\right)}^4=\left(\frac{2^4}{10^8}\right)=\left(\frac{16}{100000000}\right)=0,00000016$;

k)

$\frac{7}{10^3}=\frac{7}{10\cdot 10\cdot 10}=\frac{7}{1000}=0,007$;

l)

$\frac{7^3}{10}=\frac{7\cdot 7\cdot 7}{10}=\frac{343}{10}=34,3$;

m)

${\left(\frac{7}{10}\right)}^3=\frac{7^3}{10^3}=\frac{343}{1000}=0,343$.