Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-4}{5} - \frac{2}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
2. \(\dfrac{y^{-2}}{y^{2}}\\= y^{ -2 - 2 }= y^{-4}\\=\frac{1}{y^{4}}\\---------------\)
3. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-4}{3} - \frac{1}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
4. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{4} - \frac{1}{4} }= x^{0}\\=1\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-1}{6}}}\\= x^{ -1 - (\frac{-1}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-3}{5} - (\frac{-3}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
7. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{4} - (\frac{-4}{5}) }= y^{\frac{21}{20}}\\=\sqrt[20]{ y^{21} }=|y|.\sqrt[20]{ y }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-1}{2} - \frac{3}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{6} - (\frac{-4}{3}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
10. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{3} - (\frac{-1}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
11. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-2}{3} - \frac{4}{5} }= x^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ x^{22} }}\\=\frac{1}{x.\sqrt[15]{ x^{7} }}=\frac{1}{x.\sqrt[15]{ x^{7} }} \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{4}{5} - (\frac{-1}{3}) }= a^{\frac{17}{15}}\\=\sqrt[15]{ a^{17} }=a.\sqrt[15]{ a^{2} }\\---------------\)