Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{-1}{6}}}\\= y^{ 1 - (\frac{-1}{6}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
2. \(\dfrac{q^{2}}{q^{2}}\\= q^{ 2 - 2 }= q^{0}\\=1\\---------------\)
3. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{5}{4}}}\\= q^{ \frac{5}{3} - \frac{5}{4} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
4. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{5}{3} - (\frac{-1}{5}) }= a^{\frac{28}{15}}\\=\sqrt[15]{ a^{28} }=a.\sqrt[15]{ a^{13} }\\---------------\)
5. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{1}{5}}}\\= q^{ \frac{5}{6} - \frac{1}{5} }= q^{\frac{19}{30}}\\=\sqrt[30]{ q^{19} }\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{3}{2} - \frac{4}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-4}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{-3}{5}}}\\= x^{ 1 - (\frac{-3}{5}) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{1}{5}}}\\= q^{ 1 - \frac{1}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{-1}}\\= y^{ \frac{-1}{3} - (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{5} - (\frac{-1}{4}) }= a^{\frac{9}{20}}\\=\sqrt[20]{ a^{9} }\\---------------\)