Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{1}{2} - (\frac{-5}{6}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{2} - \frac{2}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
4. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{5}{3} - \frac{5}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
5. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-4}{5} - \frac{1}{5} }= q^{-1}\\=\frac{1}{q}\\---------------\)
6. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{1}{2} - (\frac{-1}{5}) }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-3}{5} - \frac{1}{4} }= a^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ a^{17} }}=\frac{1}{\sqrt[20]{ a^{17} }}. \color{purple}{\frac{\sqrt[20]{ a^{3} }}{\sqrt[20]{ a^{3} }}} \\=\frac{\sqrt[20]{ a^{3} }}{|a|}\\---------------\)
8. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{4} - \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-1}{4} - \frac{4}{3} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{6}}}{q^{-2}}\\= q^{ \frac{1}{6} - (-2) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)