Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{2} - \frac{1}{4} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{-2}}\\= q^{ \frac{-3}{5} - (-2) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{3}{4}}}\\= y^{ \frac{2}{5} - \frac{3}{4} }= y^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ y^{7} }}=\frac{1}{\sqrt[20]{ y^{7} }}. \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y|}\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{2}{3} - (\frac{-1}{3}) }= x^{1}\\\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
6. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{2} - (\frac{-3}{5}) }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-4}{3} - \frac{4}{5} }= y^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ y^{32} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{3}}\\---------------\)
8. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{4} - \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
9. \(\dfrac{y^{\frac{5}{6}}}{y^{-2}}\\= y^{ \frac{5}{6} - (-2) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-4}{5} - \frac{1}{3} }= q^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ q^{17} }}\\=\frac{1}{q.\sqrt[15]{ q^{2} }}=\frac{1}{q.\sqrt[15]{ q^{2} }} \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{3} - (\frac{-2}{5}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-3}{4}}}\\= q^{ -1 - (\frac{-3}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)