Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{6} - \frac{5}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{2}{3} - (\frac{-1}{5}) }= x^{\frac{13}{15}}\\=\sqrt[15]{ x^{13} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{2} - \frac{2}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{2}) }= x^{2}\\\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{-5}{6}}}\\= y^{ -1 - (\frac{-5}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-2}{3} - \frac{4}{3} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
7. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-3}{4} - (\frac{-3}{5}) }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
8. \(\dfrac{q^{\frac{5}{3}}}{q^{-1}}\\= q^{ \frac{5}{3} - (-1) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
9. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{4}{3}}}\\= a^{ \frac{2}{5} - \frac{4}{3} }= a^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ a^{14} }}=\frac{1}{\sqrt[15]{ a^{14} }}. \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{6} - (\frac{-3}{4}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{5} - \frac{1}{4} }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{-3}{2}}}\\= y^{ 1 - (\frac{-3}{2}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)