Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{3}{4}}}\\= y^{ \frac{3}{2} - \frac{3}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
2. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{5}{4} - (\frac{-2}{3}) }= q^{\frac{23}{12}}\\=\sqrt[12]{ q^{23} }=|q|.\sqrt[12]{ q^{11} }\\---------------\)
3. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-5}{6} - \frac{3}{2} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
4. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{3}{2} - \frac{5}{6} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
5. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{5}{3} - \frac{1}{6} }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
6. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{6} - (\frac{-2}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{2}{3} - (\frac{-5}{6}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
8. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{5} - \frac{2}{3} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-1}{6} - (\frac{-4}{5}) }= x^{\frac{19}{30}}\\=\sqrt[30]{ x^{19} }\\---------------\)
10. \(\dfrac{y^{\frac{-5}{2}}}{y^{1}}\\= y^{ \frac{-5}{2} - 1 }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
11. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{3}{4} - (\frac{-5}{2}) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{1}{5}}}{a^{1}}\\= a^{ \frac{1}{5} - 1 }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)