Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{2}{3} - \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{4}{5}}}\\= a^{ 1 - \frac{4}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
3. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-2}{5} - \frac{1}{5} }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
4. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{2} - \frac{1}{3} }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
5. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{4} - \frac{1}{3} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{3}{4}}}\\= q^{ \frac{3}{4} - \frac{3}{4} }= q^{0}\\=1\\---------------\)
7. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{3} - (\frac{-2}{3}) }= a^{1}\\\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-3}{5} - \frac{5}{4} }= y^{\frac{-37}{20}}\\=\frac{1}{\sqrt[20]{ y^{37} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{17} }}=\frac{1}{|y|.\sqrt[20]{ y^{17} }} \color{purple}{\frac{\sqrt[20]{ y^{3} }}{\sqrt[20]{ y^{3} }}} \\=\frac{\sqrt[20]{ y^{3} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
11. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{3} - \frac{2}{5} }= q^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ q^{11} }}=\frac{1}{\sqrt[15]{ q^{11} }}. \color{purple}{\frac{\sqrt[15]{ q^{4} }}{\sqrt[15]{ q^{4} }}} \\=\frac{\sqrt[15]{ q^{4} }}{q}\\---------------\)
12. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{5}{4} - \frac{4}{5} }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)