Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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