Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{3} - \frac{1}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{3}{5}}}\\= q^{ -1 - \frac{3}{5} }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{5} - \frac{1}{4} }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{2}{3} - \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-4}{3}}}\\= x^{ 1 - (\frac{-4}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-5}{3} - (\frac{-4}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{5} - \frac{1}{2} }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{2} - (\frac{-2}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
10. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-5}{4} - \frac{5}{6} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{2}) }= q^{1}\\\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-1}{3} - \frac{1}{6} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)