Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{2}{3}}}\\= x^{ 1 - \frac{2}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\dfrac{q^{-2}}{q^{\frac{-1}{6}}}\\= q^{ -2 - (\frac{-1}{6}) }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-1}{6} - (\frac{-4}{5}) }= a^{\frac{19}{30}}\\=\sqrt[30]{ a^{19} }\\---------------\)
4. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{5} - \frac{2}{3} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{1}{6}}}\\= a^{ 1 - \frac{1}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
6. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{2} - \frac{1}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{4}{3}}}\\= q^{ \frac{3}{4} - \frac{4}{3} }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{3}}}{a^{1}}\\= a^{ \frac{1}{3} - 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
9. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{5}{3} - (\frac{-2}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
10. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{2}{3} - \frac{2}{3} }= y^{0}\\=1\\---------------\)
11. \(\dfrac{y^{1}}{y^{2}}\\= y^{ 1 - 2 }= y^{-1}\\=\frac{1}{y}\\---------------\)
12. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)