Pentru a = 1
a² = 1
a³ = 1
[tex]pentru \: a \: = \frac{1}{2} [/tex]
[tex] {a}^{2 } = {( \frac{1}{2}) }^{2} = \frac{ {1}^{2} }{ {2}^{2} } = \frac{1}{4} [/tex]
[tex] {a}^{3} = {( \frac{1}{2} )}^{3} = \frac{ {1}^{3} }{ {2}^{3} } = \frac{1}{8} [/tex]
[tex]pentru \: a = 1 \frac{1}{3} [/tex]
[tex] {a}^{2} = {(1 \frac{1}{3} )}^{2} = (bagi \: intregii \: in \: fractie) \: { (\frac{1 \times 3 + 1}{3}) }^{2} = { (\frac{4}{3} )}^{2} = \frac{ {4}^{2} }{ {3}^{2} } = \frac{16}{9} [/tex]
[tex] {a}^{3} = {(1 \frac{1}{3}) }^{3} = (bagi \: intregii \: infractie) \: { (\frac{1 \times 3 + 1}{3} )}^{3} = { (\frac{4}{3}) }^{3} = \frac{ {4}^{3} }{ {3}^{3} } = \frac{64}{27} [/tex]
Pentru a = –1
a² = 1
a³ = –1
[tex]pentru \: a = - \frac{1}{3}[/tex]
[tex] {a}^{2} = {( - \frac{ 1}{3} )}^{2} =( nr \: negativ \: la \: putere \: para \: devine \: pozitiv) \: \frac{ {1}^{2} }{ {3}^{2} } = \frac{1}{9} [/tex]
[tex] {a}^{3 } = { (- \frac{1}{3}) }^{3} = - \frac{ {1}^{3} }{ {3}^{3} } = - \frac{1}{27} [/tex]
Pentru a = –0,2
[tex] {a}^{2} = { - 0.2}^{2} = (- {\frac{2}{10} )}^{2} = \frac{ {2}^{2} }{ {10}^{2} } = \frac{4}{100} = \frac{2}{50} = \frac{1}{15} [/tex]
[tex] {a}^{3} = { - 0.2}^{3} = { ( - \frac{2}{10}) }^{3} = - \frac{ {2}^{3} }{ {10}^{3} } = \frac{8}{1000} = \frac{4}{500} = \frac{2}{250} = \frac{1}{125} [/tex]
