Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{-5}{6}}}\\= q^{ -1 - (\frac{-5}{6}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
2. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{3} - \frac{1}{3} }= q^{0}\\=1\\---------------\)
4. \(\dfrac{q^{\frac{5}{4}}}{q^{-2}}\\= q^{ \frac{5}{4} - (-2) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{5}{6}}}\\= q^{ \frac{2}{5} - \frac{5}{6} }= q^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ q^{13} }}=\frac{1}{\sqrt[30]{ q^{13} }}. \color{purple}{\frac{\sqrt[30]{ q^{17} }}{\sqrt[30]{ q^{17} }}} \\=\frac{\sqrt[30]{ q^{17} }}{|q|}\\---------------\)
6. \(\dfrac{y^{1}}{y^{-2}}\\= y^{ 1 - (-2) }= y^{3}\\\\---------------\)
7. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{3} - \frac{2}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
8. \(\dfrac{y^{-2}}{y^{\frac{1}{3}}}\\= y^{ -2 - \frac{1}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
9. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{5}{2}}}\\= x^{ \frac{1}{5} - \frac{5}{2} }= x^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ x^{23} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{3} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{3}|}\\---------------\)
10. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{3}{2}}}\\= x^{ \frac{5}{6} - \frac{3}{2} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
11. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{1}{3} - (\frac{-5}{6}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{3} - \frac{1}{2} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)