Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{4}{5}}}{x^{2}}\\= x^{ \frac{4}{5} - 2 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{2} - \frac{1}{2} }= q^{0}\\=1\\---------------\)
3. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
4. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{3}{5} - \frac{3}{4} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{3}{5}}}\\= y^{ 1 - \frac{3}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{2}{3} - (\frac{-1}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{3}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
8. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{6} - (\frac{-1}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{y^{\frac{-4}{5}}}{y^{-1}}\\= y^{ \frac{-4}{5} - (-1) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-3}{2} - (\frac{-3}{5}) }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{3} - \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{5}{3}}}\\= a^{ \frac{1}{4} - \frac{5}{3} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)