Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-5}{3} - \frac{4}{3} }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
2. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{5}{6} - (\frac{-4}{3}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{4}{5}}}\\= a^{ -1 - \frac{4}{5} }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-1}{2} - \frac{1}{6} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
5. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{2}{5} - \frac{1}{2} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
6. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{3}{5}}}\\= q^{ \frac{1}{3} - \frac{3}{5} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{5} - \frac{1}{2} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
8. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-3}{5} - \frac{1}{4} }= x^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ x^{17} }}=\frac{1}{\sqrt[20]{ x^{17} }}. \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x|}\\---------------\)
9. \(\dfrac{a^{1}}{a^{-2}}\\= a^{ 1 - (-2) }= a^{3}\\\\---------------\)
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. \(\dfrac{a^{\frac{2}{3}}}{a^{-1}}\\= a^{ \frac{2}{3} - (-1) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{4}}}{a^{-1}}\\= a^{ \frac{1}{4} - (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)