Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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