Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{5}{3} - (\frac{-1}{2}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
2. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{6}) }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
3. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-2}{3}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
4. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{1}{6} - (\frac{-4}{5}) }= a^{\frac{29}{30}}\\=\sqrt[30]{ a^{29} }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-3}{5} - (\frac{-3}{4}) }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{-5}{3}}}\\= q^{ 1 - (\frac{-5}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{3}{2}}}{q^{-1}}\\= q^{ \frac{3}{2} - (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
8. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{5}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
9. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{3} - (\frac{-3}{5}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
11. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-5}{6} - \frac{2}{3} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)