Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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