Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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