Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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