Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{-2}}\\= y^{ \frac{1}{3} - (-2) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{2} - \frac{5}{6} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{5} - \frac{2}{3} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
5. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{4} - (\frac{-3}{5}) }= y^{\frac{17}{20}}\\=\sqrt[20]{ y^{17} }\\---------------\)
6. \(\dfrac{q^{2}}{q^{\frac{-1}{3}}}\\= q^{ 2 - (\frac{-1}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-2}{3} - \frac{1}{5} }= q^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ q^{13} }}=\frac{1}{\sqrt[15]{ q^{13} }}. \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q}\\---------------\)
8. \(\dfrac{a^{\frac{2}{5}}}{a^{1}}\\= a^{ \frac{2}{5} - 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
9. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-4}{5} - (\frac{-3}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
10. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{3}{4} - (\frac{-5}{6}) }= y^{\frac{19}{12}}\\=\sqrt[12]{ y^{19} }=|y|.\sqrt[12]{ y^{7} }\\---------------\)
11. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{3}{4} - \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
12. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{3}{2} - \frac{4}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)