Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{1}{2} - \frac{4}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{-3}{2}}}{q^{-1}}\\= q^{ \frac{-3}{2} - (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{-2}}\\= y^{ \frac{-1}{2} - (-2) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
5. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{6} - \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-3}{4} - \frac{5}{3} }= q^{\frac{-29}{12}}\\=\frac{1}{\sqrt[12]{ q^{29} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{3}|}\\---------------\)
7. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{4}{3} - \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{2} - \frac{1}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-1}{2} - \frac{3}{5} }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{2}{3} - (\frac{-1}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-4}{3}}}\\= x^{ 1 - (\frac{-4}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{-1}}\\= a^{ \frac{-1}{2} - (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)