Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{3}{2}}}{a^{-1}}\\= a^{ \frac{3}{2} - (-1) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
2. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{4}{3} - \frac{2}{5} }= a^{\frac{14}{15}}\\=\sqrt[15]{ a^{14} }\\---------------\)
3. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{4} - (\frac{-1}{5}) }= x^{\frac{9}{20}}\\=\sqrt[20]{ x^{9} }\\---------------\)
4. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{5}{4} - (\frac{-1}{5}) }= y^{\frac{29}{20}}\\=\sqrt[20]{ y^{29} }=|y|.\sqrt[20]{ y^{9} }\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{1}{3} - \frac{5}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{6} - \frac{1}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{-1}{2}}}\\= y^{ 1 - (\frac{-1}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
8. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{5} - (\frac{-1}{2}) }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)
9. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{4}{5} - \frac{3}{4} }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{5}{2} - (\frac{-5}{4}) }= y^{\frac{15}{4}}\\=\sqrt[4]{ y^{15} }=|y^{3}|.\sqrt[4]{ y^{3} }\\---------------\)
11. \(\dfrac{a^{\frac{-5}{2}}}{a^{-1}}\\= a^{ \frac{-5}{2} - (-1) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{3}{2} - \frac{1}{2} }= x^{1}\\\\---------------\)