Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{2} - \frac{2}{5} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
2. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{1}{4} - (\frac{-5}{6}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)
3. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
4. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{4} - (\frac{-5}{3}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
5. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{2} - \frac{2}{3} }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
6. \(\dfrac{q^{\frac{-3}{2}}}{q^{-1}}\\= q^{ \frac{-3}{2} - (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{-1}}\\= a^{ \frac{-1}{2} - (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
8. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{5}{2}}}\\= x^{ \frac{1}{2} - \frac{5}{2} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-1}{6} - (\frac{-3}{5}) }= x^{\frac{13}{30}}\\=\sqrt[30]{ x^{13} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{3}{4}}}\\= y^{ \frac{1}{2} - \frac{3}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
11. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{5}) }= a^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ a^{21} }}\\=\frac{1}{|a|.\sqrt[20]{ a }}=\frac{1}{|a|.\sqrt[20]{ a }} \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{6} - (\frac{-5}{6}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)