Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{-1}}\\= q^{ \frac{2}{3} - (-1) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
2. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{5}{2} - (\frac{-2}{5}) }= y^{\frac{29}{10}}\\=\sqrt[10]{ y^{29} }=|y^{2}|.\sqrt[10]{ y^{9} }\\---------------\)
3. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-2}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{2} - \frac{1}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{3}{5} - \frac{2}{3} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
6. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{3} - \frac{2}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{3} - (\frac{-3}{4}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
8. \(\dfrac{a^{-2}}{a^{\frac{5}{2}}}\\= a^{ -2 - \frac{5}{2} }= a^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ a^{9} } }\\=\frac{1}{|a^{4}|. \sqrt{ a } }=\frac{1}{|a^{4}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{5}|}\\---------------\)
9. \(\dfrac{a^{-2}}{a^{\frac{1}{2}}}\\= a^{ -2 - \frac{1}{2} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
10. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-2}{5} - \frac{3}{4} }= y^{\frac{-23}{20}}\\=\frac{1}{\sqrt[20]{ y^{23} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{3} }}=\frac{1}{|y|.\sqrt[20]{ y^{3} }} \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{1}{3}}}{x^{1}}\\= x^{ \frac{1}{3} - 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
12. \(\dfrac{q^{\frac{-5}{6}}}{q^{-1}}\\= q^{ \frac{-5}{6} - (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)