Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-2}{3} - \frac{3}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
2. \(\dfrac{y^{\frac{-5}{4}}}{y^{2}}\\= y^{ \frac{-5}{4} - 2 }= y^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ y^{13} }}\\=\frac{1}{|y^{3}|.\sqrt[4]{ y }}=\frac{1}{|y^{3}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{4}|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{3}}}{y^{1}}\\= y^{ \frac{5}{3} - 1 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{5} - \frac{1}{4} }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
5. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-3}{2} - \frac{2}{5} }= y^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{9} }}=\frac{1}{|y|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{2}{3} - (\frac{-2}{5}) }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-1}{3} - \frac{5}{2} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
8. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{5}{3} - \frac{2}{3} }= x^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{2} - \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
11. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{3}) }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{4} - \frac{2}{3} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)