Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-3}{4}}}\\= q^{ 1 - (\frac{-3}{4}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{1}}\\= a^{ \frac{1}{2} - 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
3. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{4}{3}}}\\= q^{ \frac{5}{6} - \frac{4}{3} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-1}{3} - \frac{3}{5} }= a^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ a^{14} }}=\frac{1}{\sqrt[15]{ a^{14} }}. \color{purple}{\frac{\sqrt[15]{ a }}{\sqrt[15]{ a }}} \\=\frac{\sqrt[15]{ a }}{a}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{5}}}{x^{1}}\\= x^{ \frac{-1}{5} - 1 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{2}) }= x^{0}\\=1\\---------------\)
8. \(\dfrac{x^{\frac{1}{3}}}{x^{-1}}\\= x^{ \frac{1}{3} - (-1) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
9. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-4}{3} - (\frac{-2}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{6} - \frac{5}{4} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{4}{3}}}\\= x^{ \frac{1}{4} - \frac{4}{3} }= x^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[12]{ x }}=\frac{1}{|x|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{2}|}\\---------------\)