Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{4}{5}}}{y^{-1}}\\= y^{ \frac{4}{5} - (-1) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
2. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-5}{6} - \frac{1}{5} }= q^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ q^{31} }}\\=\frac{1}{|q|.\sqrt[30]{ q }}=\frac{1}{|q|.\sqrt[30]{ q }} \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\\= y^{ \frac{1}{3} - (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-3}{5} - \frac{1}{4} }= a^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ a^{17} }}=\frac{1}{\sqrt[20]{ a^{17} }}. \color{purple}{\frac{\sqrt[20]{ a^{3} }}{\sqrt[20]{ a^{3} }}} \\=\frac{\sqrt[20]{ a^{3} }}{|a|}\\---------------\)
7. \(\dfrac{y^{\frac{-1}{6}}}{y^{-1}}\\= y^{ \frac{-1}{6} - (-1) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{5}{4}}}\\= q^{ -1 - \frac{5}{4} }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
9. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
10. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{5} - (\frac{-2}{3}) }= q^{\frac{13}{15}}\\=\sqrt[15]{ q^{13} }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-1}{6} - (\frac{-3}{2}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{5}{2}}}\\= a^{ -1 - \frac{5}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)