Werk uit m.b.v. de rekenregels
- \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{2}}}\)
- \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-3}{2}}}\)
- \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{5}}}\)
- \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-2}{5}}}\)
- \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{5}}}\)
- \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\)
- \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{2}{3}}}\)
- \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{2}{3}}}\)
- \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{6}}}\)
- \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{6}}}\)
- \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{4}{3}}}\)
- \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{3}}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{6} - (\frac{-1}{2}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}.
\color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
- \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{1}{2} - (\frac{-3}{2}) }= q^{2}\\\\---------------\)
- \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{2} - \frac{2}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
- \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{4} - (\frac{-2}{5}) }= y^{\frac{13}{20}}\\=\sqrt[20]{ y^{13} }\\---------------\)
- \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{2}{3} - \frac{2}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
- \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }}
\color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
- \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{2} - \frac{2}{3} }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }}
\color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
- \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{3} - \frac{2}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
- \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{4}{5} - (\frac{-5}{6}) }= a^{\frac{49}{30}}\\=\sqrt[30]{ a^{49} }=|a|.\sqrt[30]{ a^{19} }\\---------------\)
- \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{3}{4} - (\frac{-1}{6}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
- \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{6} - \frac{4}{3} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }}
\color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
- \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{3} - \frac{5}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)