Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{3}) }= q^{0}\\=1\\---------------\)
2. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{5}{2} - (\frac{-4}{3}) }= y^{\frac{23}{6}}\\=\sqrt[6]{ y^{23} }=|y^{3}|.\sqrt[6]{ y^{5} }\\---------------\)
3. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-5}{4} - \frac{4}{5} }= q^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ q^{41} }}\\=\frac{1}{|q^{2}|.\sqrt[20]{ q }}=\frac{1}{|q^{2}|.\sqrt[20]{ q }} \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q^{3}|}\\---------------\)
4. \(\dfrac{q^{-1}}{q^{\frac{-5}{2}}}\\= q^{ -1 - (\frac{-5}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
5. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{4} - \frac{1}{3} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{5}{3} - \frac{3}{4} }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
7. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-3}{4} - \frac{1}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{2}{5}}}\\= q^{ 1 - \frac{2}{5} }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
9. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-4}{5} - (\frac{-3}{2}) }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{6} - \frac{2}{5} }= q^{\frac{-17}{30}}\\=\frac{1}{\sqrt[30]{ q^{17} }}=\frac{1}{\sqrt[30]{ q^{17} }}. \color{purple}{\frac{\sqrt[30]{ q^{13} }}{\sqrt[30]{ q^{13} }}} \\=\frac{\sqrt[30]{ q^{13} }}{|q|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{3} - \frac{2}{5} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-3}{5} - \frac{1}{4} }= x^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ x^{17} }}=\frac{1}{\sqrt[20]{ x^{17} }}. \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x|}\\---------------\)