Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-5}{3} - (\frac{-3}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{6} - \frac{2}{3} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{5}{4} - (\frac{-4}{5}) }= q^{\frac{41}{20}}\\=\sqrt[20]{ q^{41} }=|q^{2}|.\sqrt[20]{ q }\\---------------\)
4. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{2}{5} - (\frac{-2}{3}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{5} - \frac{1}{4} }= q^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ q }}=\frac{1}{\sqrt[20]{ q }}. \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q|}\\---------------\)
6. \(\dfrac{y^{-1}}{y^{\frac{5}{3}}}\\= y^{ -1 - \frac{5}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{3} - \frac{1}{2} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{5} - (\frac{-3}{4}) }= x^{\frac{11}{20}}\\=\sqrt[20]{ x^{11} }\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{2} - \frac{2}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\dfrac{q^{\frac{2}{5}}}{q^{-1}}\\= q^{ \frac{2}{5} - (-1) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
11. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-1}{3}) }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{6} - \frac{2}{3} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)