Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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