Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{1}{6}}}\\= y^{ \frac{1}{4} - \frac{1}{6} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-2}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{6} - (\frac{-3}{4}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{1}{3}}}\\= y^{ 1 - \frac{1}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
6. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-2}{5} - (\frac{-4}{3}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
8. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{6} - \frac{1}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-4}{5}}}\\= x^{ 1 - (\frac{-4}{5}) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{-3}{5}}}\\= x^{ 1 - (\frac{-3}{5}) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{1}{4} - (\frac{-1}{6}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
12. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{3}{5} - \frac{1}{2} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)