Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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