Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{2}}}{q^{1}}\\= q^{ \frac{5}{2} - 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
2. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{5}{6}}}\\= x^{ \frac{4}{5} - \frac{5}{6} }= x^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ x }}=\frac{1}{\sqrt[30]{ x }}. \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x|}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{5} - \frac{1}{3} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{-4}{5}}}\\= y^{ -1 - (\frac{-4}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
5. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{3} - \frac{2}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
6. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{5} - \frac{1}{2} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{2} - \frac{4}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{2} - \frac{5}{6} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-5}{4} - \frac{3}{5} }= x^{\frac{-37}{20}}\\=\frac{1}{\sqrt[20]{ x^{37} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{17} }}=\frac{1}{|x|.\sqrt[20]{ x^{17} }} \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-2}{5} - \frac{5}{3} }= y^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ y^{31} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y }}=\frac{1}{y^{2}.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{3}}\\---------------\)
11. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{2}{3} - \frac{3}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{1}{4}}}\\= a^{ 1 - \frac{1}{4} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)