Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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