Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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