POTĘGA O WYKŁADNIKU CAŁKOWITYM UJEMNYM - ZADANIA
Zadanie 4
Oblicz ułamki podniesione do potęgi ujemnej: \(\left(\frac25\right)^{-1}\;,\;\left(\frac47\right)^{-2}\;,\;\left(\frac13\right)^{-3}\;,\;
\left(0,1\right)^{-1}\;,\;\left(0,2\right)^{-2}\) korzystając ze wzoru: \(\large a^{-n}=\frac1{a^n}\)
\(\displaystyle \left(\frac25\right)^{-1}=\frac1{\left(\frac25\right)^1}=
\frac1{\frac25}=1:\frac25=1\cdot\frac52=\frac52=2\frac12\)
\(\displaystyle \left(\frac47\right)^{-2}=\frac1{\left(\frac47\right)^2}=
\frac1{\frac{16}{49}}=1:\frac{16}{49}=1\cdot\frac{49}{16}=\left(\frac74\right)^2\)
\(\displaystyle \left(\frac13\right)^{-3}=\frac1{\left(\frac13\right)^3}=
\frac1{{\frac13}\cdot{\frac13}\cdot{\frac13}}=\frac1{\frac1{27}}=1:\frac1{27}=1\cdot\frac{27}1=27\)
\(\displaystyle \left(0,1\right)^{-1}=\frac1{\left(0,1\right)^1}=
\frac1{\left({\frac1{10}}\right)^1}=\frac1{\frac1{10}}=1:\frac1{10}=1\cdot\frac{10}1=10\)
\(\displaystyle \left(0,2\right)^{-2}=\frac1{\left(0,2\right)^2}=\frac1{\left({\frac2{10}}\right)^2}=
\frac1{{\frac2{10}}\cdot{\frac2{10}}}=\frac1{\frac4{100}}=1:\frac4{100}=1\cdot\frac{100}4=25\)
