Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-1}{6} - (\frac{-1}{5}) }= a^{\frac{1}{30}}\\=\sqrt[30]{ a }\\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-3}{5} - \frac{3}{2} }= q^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ q^{21} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q }}=\frac{1}{|q^{2}|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{3}|}\\---------------\)
3. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{5}{4} - \frac{2}{3} }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
4. \(\dfrac{q^{\frac{5}{3}}}{q^{-1}}\\= q^{ \frac{5}{3} - (-1) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{5}{4}}}{y^{1}}\\= y^{ \frac{5}{4} - 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{4}{3}}}{x^{1}}\\= x^{ \frac{4}{3} - 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-2}{5} - (\frac{-5}{6}) }= x^{\frac{13}{30}}\\=\sqrt[30]{ x^{13} }\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{-4}{5}}}\\= y^{ 1 - (\frac{-4}{5}) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
10. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{3} - \frac{2}{3} }= y^{1}\\\\---------------\)
11. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{4} - (\frac{-2}{3}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
12. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{5}{6} - \frac{5}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)