Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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