Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
2. \(\dfrac{x^{\frac{1}{5}}}{x^{-1}}\\= x^{ \frac{1}{5} - (-1) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
3. \(\dfrac{x^{-1}}{x^{2}}\\= x^{ -1 - 2 }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
4. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-4}{3} - (\frac{-2}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
5. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{5} - (\frac{-1}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
6. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{3}{2} - \frac{2}{5} }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{5}{6}}}\\= x^{ -1 - \frac{5}{6} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{3}{2} - (\frac{-5}{6}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{1}{3}}}\\= q^{ 1 - \frac{1}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{2}) }= q^{0}\\=1\\---------------\)
11. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-5}{6} - \frac{5}{6} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-1}{5} - \frac{3}{4} }= a^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ a^{19} }}=\frac{1}{\sqrt[20]{ a^{19} }}. \color{purple}{\frac{\sqrt[20]{ a }}{\sqrt[20]{ a }}} \\=\frac{\sqrt[20]{ a }}{|a|}\\---------------\)