Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{5}}}{a^{-2}}\\= a^{ \frac{-1}{5} - (-2) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
2. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-5}{2} - \frac{2}{5} }= a^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ a^{29} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a^{9} }}=\frac{1}{|a^{2}|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{3}|}\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{-3}{4}}}\\= y^{ 1 - (\frac{-3}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
4. \(\dfrac{x^{1}}{x^{-2}}\\= x^{ 1 - (-2) }= x^{3}\\\\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{-1}{3}}}\\= q^{ -1 - (\frac{-1}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{6}}}{y^{1}}\\= y^{ \frac{-5}{6} - 1 }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{1}{4} - \frac{4}{5} }= q^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ q^{11} }}=\frac{1}{\sqrt[20]{ q^{11} }}. \color{purple}{\frac{\sqrt[20]{ q^{9} }}{\sqrt[20]{ q^{9} }}} \\=\frac{\sqrt[20]{ q^{9} }}{|q|}\\---------------\)
8. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{4}{3} - (\frac{-1}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{2} - \frac{2}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-4}{3} - (\frac{-5}{2}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{3} - \frac{3}{5} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{4} - \frac{1}{2} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)