Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{2}{3} - \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{4}{3}}}\\= y^{ 1 - \frac{4}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
3. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{3}{4} - (\frac{-5}{6}) }= x^{\frac{19}{12}}\\=\sqrt[12]{ x^{19} }=|x|.\sqrt[12]{ x^{7} }\\---------------\)
4. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{6} - (\frac{-1}{5}) }= x^{\frac{11}{30}}\\=\sqrt[30]{ x^{11} }\\---------------\)
5. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-4}{3} - (\frac{-2}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-5}{2}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{2}{3} - \frac{2}{5} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{5} - (\frac{-2}{5}) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{4}{5}}}\\= q^{ -1 - \frac{4}{5} }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{4} - (\frac{-1}{2}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
12. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{2}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)