Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{3}{5} - (\frac{-1}{2}) }= q^{\frac{11}{10}}\\=\sqrt[10]{ q^{11} }=|q|.\sqrt[10]{ q }\\---------------\)
2. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{3}{4}}}\\= q^{ \frac{3}{4} - \frac{3}{4} }= q^{0}\\=1\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{-1}{4}}}\\= y^{ -1 - (\frac{-1}{4}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{1}{2} - (\frac{-1}{6}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-3}{4} - (\frac{-3}{5}) }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{2} - (\frac{-3}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
8. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{5} - \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
9. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-3}{5} - (\frac{-5}{6}) }= q^{\frac{7}{30}}\\=\sqrt[30]{ q^{7} }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
11. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{4}{3} - \frac{1}{4} }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-5}{6} - \frac{5}{6} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)