Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{3}{5}}}\\= y^{ 1 - \frac{3}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{2} - (\frac{-2}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
4. \(\dfrac{x^{-2}}{x^{\frac{1}{3}}}\\= x^{ -2 - \frac{1}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
5. \(\dfrac{x^{1}}{x^{\frac{1}{5}}}\\= x^{ 1 - \frac{1}{5} }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
6. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{5}{2}}}\\= x^{ \frac{1}{2} - \frac{5}{2} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{5}{6}}}\\= x^{ \frac{2}{5} - \frac{5}{6} }= x^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ x^{13} }}=\frac{1}{\sqrt[30]{ x^{13} }}. \color{purple}{\frac{\sqrt[30]{ x^{17} }}{\sqrt[30]{ x^{17} }}} \\=\frac{\sqrt[30]{ x^{17} }}{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-1}{6} - (\frac{-5}{4}) }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
10. \(\dfrac{q^{\frac{5}{3}}}{q^{-1}}\\= q^{ \frac{5}{3} - (-1) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{2}{3}}}\\= a^{ 1 - \frac{2}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)