Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-2}}{x^{-1}}\\= x^{ -2 - (-1) }= x^{-1}\\=\frac{1}{x}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{5}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{2}{3} - (\frac{-3}{4}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)
4. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{5}{6} - (\frac{-5}{2}) }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
5. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-4}{3} - (\frac{-1}{6}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-1}{6} - \frac{3}{4} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
7. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{3}{2} - \frac{2}{5} }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
8. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{4}{5} - (\frac{-5}{2}) }= x^{\frac{33}{10}}\\=\sqrt[10]{ x^{33} }=|x^{3}|.\sqrt[10]{ x^{3} }\\---------------\)
9. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{4}{3} - \frac{5}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{4}{5}}}\\= a^{ \frac{2}{5} - \frac{4}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
11. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{4}{5}}}\\= x^{ 1 - \frac{4}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)