Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{5}{3} - (\frac{-5}{6}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
2. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{5} - \frac{2}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-4}{3} - \frac{4}{5} }= a^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ a^{32} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{3}}\\---------------\)
4. \(\dfrac{a^{\frac{-5}{6}}}{a^{-1}}\\= a^{ \frac{-5}{6} - (-1) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{4} - (\frac{-1}{3}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
6. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{6}) }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{6}}}{x^{-2}}\\= x^{ \frac{-1}{6} - (-2) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
9. \(\dfrac{y^{\frac{1}{3}}}{y^{1}}\\= y^{ \frac{1}{3} - 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
10. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-4}{5} - (\frac{-1}{4}) }= q^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ q^{11} }}=\frac{1}{\sqrt[20]{ q^{11} }}. \color{purple}{\frac{\sqrt[20]{ q^{9} }}{\sqrt[20]{ q^{9} }}} \\=\frac{\sqrt[20]{ q^{9} }}{|q|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
12. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-4}{3} - \frac{3}{5} }= q^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ q^{29} }}\\=\frac{1}{q.\sqrt[15]{ q^{14} }}=\frac{1}{q.\sqrt[15]{ q^{14} }} \color{purple}{\frac{\sqrt[15]{ q }}{\sqrt[15]{ q }}} \\=\frac{\sqrt[15]{ q }}{q^{2}}\\---------------\)