Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{2}{5}}}{y^{-1}}\\= y^{ \frac{2}{5} - (-1) }= y^{\frac{7}{5}}\\=\sqrt[5]{ y^{7} }=y.\sqrt[5]{ y^{2} }\\---------------\)
2. \(\dfrac{q^{-2}}{q^{\frac{-3}{2}}}\\= q^{ -2 - (\frac{-3}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{2}{3} - \frac{5}{6} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
4. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{2}{5}}}\\= y^{ \frac{5}{6} - \frac{2}{5} }= y^{\frac{13}{30}}\\=\sqrt[30]{ y^{13} }\\---------------\)
5. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{1}{5}}}\\= y^{ \frac{5}{4} - \frac{1}{5} }= y^{\frac{21}{20}}\\=\sqrt[20]{ y^{21} }=|y|.\sqrt[20]{ y }\\---------------\)
6. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-2}{3} - \frac{2}{5} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{-1}{4}}}\\= q^{ -1 - (\frac{-1}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{-1}{4}}}\\= q^{ 1 - (\frac{-1}{4}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{2} - \frac{1}{4} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{5}{4}}}\\= a^{ 1 - \frac{5}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{2} - \frac{5}{6} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{2} - (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)