Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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