Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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