Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-4}{5}) }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
2. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-5}{4} - (\frac{-3}{5}) }= y^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ y^{13} }}=\frac{1}{\sqrt[20]{ y^{13} }}. \color{purple}{\frac{\sqrt[20]{ y^{7} }}{\sqrt[20]{ y^{7} }}} \\=\frac{\sqrt[20]{ y^{7} }}{|y|}\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{-1}}\\= q^{ \frac{2}{5} - (-1) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
4. \(\dfrac{a^{-2}}{a^{\frac{-1}{2}}}\\= a^{ -2 - (\frac{-1}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{5}}}{y^{1}}\\= y^{ \frac{1}{5} - 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
6. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-4}{3} - (\frac{-2}{5}) }= a^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ a^{14} }}=\frac{1}{\sqrt[15]{ a^{14} }}. \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a}\\---------------\)
7. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{3}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{1}{5} - \frac{4}{5} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
9. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-3}{4} - \frac{1}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-3}{4} - (\frac{-3}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
11. \(\dfrac{y^{1}}{y^{\frac{-3}{2}}}\\= y^{ 1 - (\frac{-3}{2}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
12. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-5}{4} - \frac{1}{6} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)