Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{3} - \frac{1}{4} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
2. \(\dfrac{x^{-2}}{x^{\frac{1}{4}}}\\= x^{ -2 - \frac{1}{4} }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{6} - \frac{1}{2} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{-1}{3}}}\\= x^{ -1 - (\frac{-1}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{5} - \frac{5}{3} }= a^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ a^{28} }}\\=\frac{1}{a.\sqrt[15]{ a^{13} }}=\frac{1}{a.\sqrt[15]{ a^{13} }} \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{5}{2} - \frac{3}{5} }= x^{\frac{19}{10}}\\=\sqrt[10]{ x^{19} }=|x|.\sqrt[10]{ x^{9} }\\---------------\)
7. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{4}{3} - \frac{2}{5} }= a^{\frac{14}{15}}\\=\sqrt[15]{ a^{14} }\\---------------\)
8. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-4}{3} - \frac{4}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-3}{2} - \frac{1}{5} }= y^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{7} }}=\frac{1}{|y|.\sqrt[10]{ y^{7} }} \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{2}{5}}}\\= a^{ 1 - \frac{2}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{-4}{3}}}{q^{-1}}\\= q^{ \frac{-4}{3} - (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{6} - (\frac{-5}{4}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)