Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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