Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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