Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{3}{4} - (\frac{-1}{4}) }= q^{1}\\\\---------------\)
2. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{6} - (\frac{-2}{5}) }= x^{\frac{7}{30}}\\=\sqrt[30]{ x^{7} }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-3}{2} - \frac{4}{3} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
4. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{2}{3} - \frac{4}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
5. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-5}{6} - \frac{5}{3} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{4} - (\frac{-1}{3}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
7. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{1}{3} - \frac{4}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
8. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{3}{5} - (\frac{-2}{3}) }= a^{\frac{19}{15}}\\=\sqrt[15]{ a^{19} }=a.\sqrt[15]{ a^{4} }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{3} - \frac{4}{5} }= a^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ a^{17} }}\\=\frac{1}{a.\sqrt[15]{ a^{2} }}=\frac{1}{a.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{3}{2}}}{q^{2}}\\= q^{ \frac{3}{2} - 2 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{5} - (\frac{-2}{5}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)