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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{6}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{2}}\\= q^{ \frac{-1}{2} - 2 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{6} - (\frac{-3}{4}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-5}{4} - (\frac{-4}{5}) }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{3}{2}}}{q^{-1}}\\= q^{ \frac{3}{2} - (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{4} - \frac{2}{3} }= q^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ q^{11} }}=\frac{1}{\sqrt[12]{ q^{11} }}. \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q|}\\---------------\)
8. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-5}{6} - \frac{1}{4} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{6} - (\frac{-2}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-1}{3} - \frac{4}{3} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{4}{3} - (\frac{-5}{4}) }= y^{\frac{31}{12}}\\=\sqrt[12]{ y^{31} }=|y^{2}|.\sqrt[12]{ y^{7} }\\---------------\)
12. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-3}{2} - \frac{3}{4} }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)