Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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