Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-1}{5}}}\\= a^{ 1 - (\frac{-1}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{4}{3} - \frac{2}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{2}}\\= q^{ \frac{-2}{3} - 2 }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
4. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{2}{3} - \frac{1}{4} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{3}{2} - \frac{3}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
6. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{3}{2} - \frac{4}{5} }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
7. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-5}{6} - \frac{5}{4} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{2}{5} - \frac{1}{3} }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{2} - \frac{1}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
10. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-3}{5} - \frac{1}{3} }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
11. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{4}) }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{2} - \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)