Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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