Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{2}}{y^{\frac{1}{2}}}\\= y^{ 2 - \frac{1}{2} }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{3}{5}}}\\= y^{ 1 - \frac{3}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{2}{5} - \frac{5}{3} }= x^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ x^{19} }}\\=\frac{1}{x.\sqrt[15]{ x^{4} }}=\frac{1}{x.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{5}{6}}}{y^{1}}\\= y^{ \frac{5}{6} - 1 }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{6}}}\\= q^{ \frac{3}{4} - \frac{1}{6} }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
6. \(\dfrac{a^{2}}{a^{\frac{3}{2}}}\\= a^{ 2 - \frac{3}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
7. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{5}{4} - \frac{2}{5} }= a^{\frac{17}{20}}\\=\sqrt[20]{ a^{17} }\\---------------\)
8. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{4} - (\frac{-3}{4}) }= a^{1}\\\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{-1}{5}}}\\= q^{ -1 - (\frac{-1}{5}) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
10. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{3}{4} - \frac{1}{3} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{5}{3} - \frac{3}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)