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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-3}{2} - \frac{3}{4} }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
2. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{4}{5} - (\frac{-5}{6}) }= q^{\frac{49}{30}}\\=\sqrt[30]{ q^{49} }=|q|.\sqrt[30]{ q^{19} }\\---------------\)
3. \(\dfrac{x^{-2}}{x^{1}}\\= x^{ -2 - 1 }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
4. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{3}{2} - (\frac{-4}{3}) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{2}{3} - (\frac{-4}{3}) }= q^{2}\\\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{1}}\\= y^{ \frac{-1}{6} - 1 }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{4}{5}}}{q^{1}}\\= q^{ \frac{4}{5} - 1 }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-1}{3} - (\frac{-5}{6}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{4}{3} - (\frac{-3}{2}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{y^{\frac{-5}{4}}}{y^{1}}\\= y^{ \frac{-5}{4} - 1 }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{2} - \frac{5}{3} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
12. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{4}) }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)