Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{1}{3}}}\\= q^{ 1 - \frac{1}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
2. \(\dfrac{x^{1}}{x^{\frac{-1}{3}}}\\= x^{ 1 - (\frac{-1}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
3. \(\dfrac{y^{\frac{-5}{6}}}{y^{1}}\\= y^{ \frac{-5}{6} - 1 }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{5}{6}}}\\= x^{ \frac{1}{3} - \frac{5}{6} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
5. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-4}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
6. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-1}{3} - \frac{4}{5} }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{5}) }= q^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ q^{7} }}=\frac{1}{\sqrt[15]{ q^{7} }}. \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q}\\---------------\)
8. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{5}{3} - \frac{1}{4} }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
9. \(\dfrac{x^{1}}{x^{-2}}\\= x^{ 1 - (-2) }= x^{3}\\\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{2} - (\frac{-5}{4}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-1}{5} - \frac{1}{6} }= y^{\frac{-11}{30}}\\=\frac{1}{\sqrt[30]{ y^{11} }}=\frac{1}{\sqrt[30]{ y^{11} }}. \color{purple}{\frac{\sqrt[30]{ y^{19} }}{\sqrt[30]{ y^{19} }}} \\=\frac{\sqrt[30]{ y^{19} }}{|y|}\\---------------\)
12. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-4}{3} - (\frac{-5}{6}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)