Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{1}}\\= a^{ \frac{1}{2} - 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{1}{3}}}\\= a^{ 1 - \frac{1}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{3} - \frac{2}{3} }= y^{1}\\\\---------------\)
4. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{2} - (\frac{-2}{3}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
5. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{2}{5} - (\frac{-5}{4}) }= y^{\frac{33}{20}}\\=\sqrt[20]{ y^{33} }=|y|.\sqrt[20]{ y^{13} }\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{5}{6}}}\\= q^{ 1 - \frac{5}{6} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-1}{2} - \frac{4}{5} }= y^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{3} }}=\frac{1}{|y|.\sqrt[10]{ y^{3} }} \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{5}}}{x^{1}}\\= x^{ \frac{1}{5} - 1 }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
10. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-4}{5} - \frac{1}{4} }= x^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ x^{21} }}\\=\frac{1}{|x|.\sqrt[20]{ x }}=\frac{1}{|x|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{4}{5} - \frac{5}{3} }= y^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ y^{13} }}=\frac{1}{\sqrt[15]{ y^{13} }}. \color{purple}{\frac{\sqrt[15]{ y^{2} }}{\sqrt[15]{ y^{2} }}} \\=\frac{\sqrt[15]{ y^{2} }}{y}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{4}) }= q^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ q^{7} }}=\frac{1}{\sqrt[20]{ q^{7} }}. \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q|}\\---------------\)