Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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