Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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