Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{3} - (\frac{-3}{5}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
2. \(\dfrac{q^{\frac{-5}{6}}}{q^{-1}}\\= q^{ \frac{-5}{6} - (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
3. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{4} - (\frac{-3}{5}) }= y^{\frac{17}{20}}\\=\sqrt[20]{ y^{17} }\\---------------\)
4. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{2}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{6} - \frac{5}{6} }= y^{-1}\\=\frac{1}{y}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{5}{4}}}\\= q^{ -1 - \frac{5}{4} }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-1}{3} - (\frac{-3}{4}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{5} - \frac{2}{3} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{4} - \frac{2}{5} }= a^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ a^{13} }}=\frac{1}{\sqrt[20]{ a^{13} }}. \color{purple}{\frac{\sqrt[20]{ a^{7} }}{\sqrt[20]{ a^{7} }}} \\=\frac{\sqrt[20]{ a^{7} }}{|a|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-1}{2} - \frac{5}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-5}{4} - (\frac{-4}{3}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)