Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

1. \(\dfrac{y^{\frac{-4}{5}}}{y^{-1}}\)
2. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{5}}}\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{3}{4}}}\)
4. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{3}{4}}}\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{2}}}\)
6. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{5}}}\)
7. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{4}{3}}}\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{3}}}\)
9. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{3}}}\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{3}}}\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{5}}}{y^{-1}}\\= y^{ \frac{-4}{5} - (-1) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
2. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{5}{3} - (\frac{-1}{5}) }= a^{\frac{28}{15}}\\=\sqrt[15]{ a^{28} }=a.\sqrt[15]{ a^{13} }\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{3}{4}}}\\= q^{ \frac{2}{5} - \frac{3}{4} }= q^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ q^{7} }}=\frac{1}{\sqrt[20]{ q^{7} }}. \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q|}\\---------------\)
4. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{3}{4}}}\\= q^{ \frac{1}{4} - \frac{3}{4} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{2} - \frac{3}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{1}{6} - (\frac{-1}{5}) }= q^{\frac{11}{30}}\\=\sqrt[30]{ q^{11} }\\---------------\)
7. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-4}{5} - \frac{4}{3} }= q^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ q^{32} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[15]{ q^{2} }} \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q^{3}}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{2} - (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{2} - \frac{1}{3} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{2}{3} - \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)