Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-5}{3} - \frac{4}{3} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
2. \(\dfrac{q^{\frac{3}{5}}}{q^{1}}\\= q^{ \frac{3}{5} - 1 }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{6} - \frac{1}{3} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
4. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-4}{3} - (\frac{-5}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{3} - \frac{2}{5} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{3}{4} - \frac{1}{2} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{2} - \frac{1}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{4} - \frac{1}{3} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{4}{5} - (\frac{-3}{2}) }= x^{\frac{23}{10}}\\=\sqrt[10]{ x^{23} }=|x^{2}|.\sqrt[10]{ x^{3} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{3} - \frac{5}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{-1}}\\= a^{ \frac{-1}{2} - (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{1}{5} - (\frac{-1}{6}) }= y^{\frac{11}{30}}\\=\sqrt[30]{ y^{11} }\\---------------\)