Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{6} - (\frac{-2}{3}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{3} - \frac{1}{3} }= a^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{5}{4} - \frac{1}{4} }= y^{1}\\\\---------------\)
4. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-4}{5} - (\frac{-1}{6}) }= x^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ x^{19} }}=\frac{1}{\sqrt[30]{ x^{19} }}. \color{purple}{\frac{\sqrt[30]{ x^{11} }}{\sqrt[30]{ x^{11} }}} \\=\frac{\sqrt[30]{ x^{11} }}{|x|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{1}{3} - (\frac{-3}{4}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-4}{5} - (\frac{-1}{4}) }= q^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ q^{11} }}=\frac{1}{\sqrt[20]{ q^{11} }}. \color{purple}{\frac{\sqrt[20]{ q^{9} }}{\sqrt[20]{ q^{9} }}} \\=\frac{\sqrt[20]{ q^{9} }}{|q|}\\---------------\)
7. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-5}{2} - \frac{2}{3} }= q^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ q^{19} }}\\=\frac{1}{|q^{3}|.\sqrt[6]{ q }}=\frac{1}{|q^{3}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{4}|}\\---------------\)
8. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{5}{2} - \frac{5}{6} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{2} - (\frac{-2}{3}) }= y^{\frac{19}{6}}\\=\sqrt[6]{ y^{19} }=|y^{3}|.\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{-5}{6}}}\\= y^{ -1 - (\frac{-5}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
11. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{5}}}\\= y^{ \frac{4}{5} - \frac{1}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{4} - (\frac{-1}{2}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)