Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{3}{5}}}\\= q^{ 1 - \frac{3}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
2. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{4}{5} - (\frac{-4}{3}) }= a^{\frac{32}{15}}\\=\sqrt[15]{ a^{32} }=a^{2}.\sqrt[15]{ a^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{2}{5}}}{x^{-2}}\\= x^{ \frac{2}{5} - (-2) }= x^{\frac{12}{5}}\\=\sqrt[5]{ x^{12} }=x^{2}.\sqrt[5]{ x^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{5} - (\frac{-1}{2}) }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-5}{2} - \frac{1}{4} }= a^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ a^{11} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{3}|}\\---------------\)
7. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{2}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{4}{3} - \frac{2}{5} }= a^{\frac{14}{15}}\\=\sqrt[15]{ a^{14} }\\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{3} - \frac{1}{6} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-4}{5} - \frac{1}{5} }= a^{-1}\\=\frac{1}{a}\\---------------\)
12. \(\dfrac{x^{-2}}{x^{1}}\\= x^{ -2 - 1 }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)