Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{4}}}{q^{1}}\\= q^{ \frac{-5}{4} - 1 }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(\dfrac{x^{\frac{1}{3}}}{x^{2}}\\= x^{ \frac{1}{3} - 2 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{6}}}{q^{2}}\\= q^{ \frac{-5}{6} - 2 }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{2}{3} - (\frac{-5}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-3}{2} - (\frac{-2}{5}) }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{2} - (\frac{-1}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
8. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{3}{5} - \frac{1}{4} }= x^{\frac{7}{20}}\\=\sqrt[20]{ x^{7} }\\---------------\)
9. \(\dfrac{y^{\frac{4}{3}}}{y^{1}}\\= y^{ \frac{4}{3} - 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{-5}{6}}}\\= x^{ -1 - (\frac{-5}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{2}{3}}}\\= a^{ 1 - \frac{2}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{y^{-2}}{y^{\frac{-2}{3}}}\\= y^{ -2 - (\frac{-2}{3}) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)