Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{2}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{3} - (\frac{-1}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{-3}{4}}}\\= a^{ -1 - (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{2}{3} - \frac{4}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
6. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{4} - (\frac{-1}{3}) }= y^{\frac{19}{12}}\\=\sqrt[12]{ y^{19} }=|y|.\sqrt[12]{ y^{7} }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{3} - \frac{1}{2} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
8. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{4}{3} - (\frac{-2}{3}) }= a^{2}\\\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{-5}{6}}}\\= y^{ 1 - (\frac{-5}{6}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-3}{2}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
11. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{2}{5} - (\frac{-1}{2}) }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{1}}\\= a^{ \frac{-4}{3} - 1 }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)