Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-1}{5} - (\frac{-3}{2}) }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-5}{3} - \frac{1}{2} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
3. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-2}{5} - (\frac{-4}{5}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
4. \(\dfrac{y^{-2}}{y^{\frac{-5}{3}}}\\= y^{ -2 - (\frac{-5}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\dfrac{a^{1}}{a^{2}}\\= a^{ 1 - 2 }= a^{-1}\\=\frac{1}{a}\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
7. \(\dfrac{y^{\frac{1}{6}}}{y^{-1}}\\= y^{ \frac{1}{6} - (-1) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-2}{5} - \frac{5}{4} }= x^{\frac{-33}{20}}\\=\frac{1}{\sqrt[20]{ x^{33} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{13} }}=\frac{1}{|x|.\sqrt[20]{ x^{13} }} \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{5}{2}}}\\= x^{ \frac{5}{4} - \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{q^{1}}{q^{\frac{1}{4}}}\\= q^{ 1 - \frac{1}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{4} - (\frac{-1}{2}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
12. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{2} - \frac{1}{3} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)