Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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