Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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