Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{2} - \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{2}{3} - (\frac{-1}{6}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
3. \(\dfrac{y^{\frac{4}{3}}}{y^{-1}}\\= y^{ \frac{4}{3} - (-1) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{-3}{5}}}\\= y^{ 1 - (\frac{-3}{5}) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-1}{3} - \frac{4}{5} }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{3}{2} - (\frac{-1}{3}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{3} - \frac{5}{3} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{4} - (\frac{-1}{3}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
11. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{5}{4} - (\frac{-4}{3}) }= y^{\frac{31}{12}}\\=\sqrt[12]{ y^{31} }=|y^{2}|.\sqrt[12]{ y^{7} }\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)