Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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