Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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