Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-3}{4} - \frac{3}{2} }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{4}}}{y^{-1}}\\= y^{ \frac{-1}{4} - (-1) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
3. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-4}{3} - \frac{5}{2} }= x^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ x^{23} }}\\=\frac{1}{|x^{3}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{3}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{4}|}\\---------------\)
4. \(\dfrac{y^{\frac{5}{6}}}{y^{1}}\\= y^{ \frac{5}{6} - 1 }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{3}{5} - (\frac{-1}{3}) }= q^{\frac{14}{15}}\\=\sqrt[15]{ q^{14} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{5}{2}}}\\= x^{ \frac{5}{2} - \frac{5}{2} }= x^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-3}{4} - (\frac{-2}{5}) }= y^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ y^{7} }}=\frac{1}{\sqrt[20]{ y^{7} }}. \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y|}\\---------------\)
9. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{2}{5} - (\frac{-2}{5}) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{2}{3} - (\frac{-3}{4}) }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{2}{3}}}{x^{1}}\\= x^{ \frac{2}{3} - 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{6}}}{q^{1}}\\= q^{ \frac{-1}{6} - 1 }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)