Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-5}{3} - \frac{2}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
3. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{1}{5} - (\frac{-5}{2}) }= x^{\frac{27}{10}}\\=\sqrt[10]{ x^{27} }=|x^{2}|.\sqrt[10]{ x^{7} }\\---------------\)
4. \(\dfrac{a^{\frac{1}{3}}}{a^{-1}}\\= a^{ \frac{1}{3} - (-1) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{2}{3}}}\\= a^{ 1 - \frac{2}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{x^{\frac{-2}{5}}}{x^{1}}\\= x^{ \frac{-2}{5} - 1 }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{6}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
8. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{6} - (\frac{-1}{3}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\dfrac{a^{\frac{1}{4}}}{a^{-1}}\\= a^{ \frac{1}{4} - (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
10. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{2} - (\frac{-2}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{-2}{3}}}\\= q^{ -1 - (\frac{-2}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{4}) }= a^{0}\\=1\\---------------\)