Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{3}{2} - \frac{5}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{2}{3} - (\frac{-3}{5}) }= q^{\frac{19}{15}}\\=\sqrt[15]{ q^{19} }=q.\sqrt[15]{ q^{4} }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-1}{3} - \frac{1}{5} }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
4. \(\dfrac{q^{\frac{3}{4}}}{q^{2}}\\= q^{ \frac{3}{4} - 2 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{2}{5} - (\frac{-3}{4}) }= y^{\frac{23}{20}}\\=\sqrt[20]{ y^{23} }=|y|.\sqrt[20]{ y^{3} }\\---------------\)
6. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{3}{4} - \frac{2}{3} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{-1}}\\= q^{ \frac{1}{2} - (-1) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-1}{3} - \frac{1}{4} }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{1}{2} - (\frac{-4}{3}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-1}{6} - \frac{3}{4} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
12. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{3} - (\frac{-1}{2}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)