Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-2}{5} - \frac{1}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{a^{\frac{-3}{4}}}{a^{-2}}\\= a^{ \frac{-3}{4} - (-2) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{x^{\frac{-2}{5}}}{x^{-1}}\\= x^{ \frac{-2}{5} - (-1) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-1}{4} - \frac{1}{4} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{-2}}\\= x^{ \frac{1}{3} - (-2) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{y^{\frac{-4}{5}}}{y^{1}}\\= y^{ \frac{-4}{5} - 1 }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{1}{6}}}\\= q^{ \frac{4}{5} - \frac{1}{6} }= q^{\frac{19}{30}}\\=\sqrt[30]{ q^{19} }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{2}}}{a^{-1}}\\= a^{ \frac{-5}{2} - (-1) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{-2}}{q^{\frac{-5}{3}}}\\= q^{ -2 - (\frac{-5}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-5}{3} - (\frac{-4}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{5} - \frac{5}{4} }= q^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ q^{29} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{9} }}=\frac{1}{|q|.\sqrt[20]{ q^{9} }} \color{purple}{\frac{\sqrt[20]{ q^{11} }}{\sqrt[20]{ q^{11} }}} \\=\frac{\sqrt[20]{ q^{11} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{6} - \frac{2}{5} }= q^{\frac{-17}{30}}\\=\frac{1}{\sqrt[30]{ q^{17} }}=\frac{1}{\sqrt[30]{ q^{17} }}. \color{purple}{\frac{\sqrt[30]{ q^{13} }}{\sqrt[30]{ q^{13} }}} \\=\frac{\sqrt[30]{ q^{13} }}{|q|}\\---------------\)