Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{1}{3} - (\frac{-5}{6}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{a^{\frac{3}{4}}}{a^{1}}\\= a^{ \frac{3}{4} - 1 }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{-3}{5}}}\\= y^{ 1 - (\frac{-3}{5}) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-2}{3} - \frac{1}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-1}{2} - \frac{1}{6} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
6. \(\dfrac{x^{\frac{-3}{4}}}{x^{-2}}\\= x^{ \frac{-3}{4} - (-2) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-5}{4} - \frac{1}{5} }= y^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ y^{29} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{9} }}=\frac{1}{|y|.\sqrt[20]{ y^{9} }} \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{5}{3} - \frac{1}{4} }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{6} - \frac{5}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
11. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{4}{5} - \frac{5}{4} }= a^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ a^{9} }}=\frac{1}{\sqrt[20]{ a^{9} }}. \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a|}\\---------------\)
12. \(\dfrac{q^{-2}}{q^{\frac{5}{2}}}\\= q^{ -2 - \frac{5}{2} }= q^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ q^{9} } }\\=\frac{1}{|q^{4}|. \sqrt{ q } }=\frac{1}{|q^{4}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{5}|}\\---------------\)