Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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