Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{6}}}{x^{2}}\\= x^{ \frac{5}{6} - 2 }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{3}{5}}}{x^{1}}\\= x^{ \frac{3}{5} - 1 }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
3. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-2}{5} - (\frac{-3}{2}) }= y^{\frac{11}{10}}\\=\sqrt[10]{ y^{11} }=|y|.\sqrt[10]{ y }\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{2} - (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
5. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{5}{6} - (\frac{-1}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{-1}}\\= q^{ \frac{-1}{2} - (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\dfrac{y^{\frac{5}{6}}}{y^{1}}\\= y^{ \frac{5}{6} - 1 }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
9. \(\dfrac{a^{2}}{a^{\frac{2}{3}}}\\= a^{ 2 - \frac{2}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{5}{3} - (\frac{-3}{2}) }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)