Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{2} - \frac{1}{6} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{q^{\frac{5}{2}}}{q^{1}}\\= q^{ \frac{5}{2} - 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-1}{2} - \frac{4}{3} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{3} - \frac{1}{3} }= a^{0}\\=1\\---------------\)
5. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{5}{2} - (\frac{-1}{4}) }= x^{\frac{11}{4}}\\=\sqrt[4]{ x^{11} }=|x^{2}|.\sqrt[4]{ x^{3} }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{5} - \frac{5}{6} }= q^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ q^{31} }}\\=\frac{1}{|q|.\sqrt[30]{ q }}=\frac{1}{|q|.\sqrt[30]{ q }} \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{1}{2} - \frac{4}{5} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{-2}{3}}}{x^{1}}\\= x^{ \frac{-2}{3} - 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{4}{3} - \frac{3}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{2}{3} - \frac{4}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\dfrac{y^{1}}{y^{\frac{-4}{3}}}\\= y^{ 1 - (\frac{-4}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
12. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)