Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-2}{5} - \frac{3}{2} }= y^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{9} }}=\frac{1}{|y|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-5}{3} - \frac{5}{2} }= y^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ y^{25} }}\\=\frac{1}{|y^{4}|.\sqrt[6]{ y }}=\frac{1}{|y^{4}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{5}|}\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{-4}{3}}}\\= x^{ 1 - (\frac{-4}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{3} - \frac{1}{2} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{3}{2} - (\frac{-2}{5}) }= a^{\frac{19}{10}}\\=\sqrt[10]{ a^{19} }=|a|.\sqrt[10]{ a^{9} }\\---------------\)
6. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-4}{3} - \frac{5}{6} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{2}{3} - \frac{5}{4} }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{6}}}{q^{2}}\\= q^{ \frac{1}{6} - 2 }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{3} - \frac{5}{6} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
10. \(\dfrac{x^{\frac{-3}{4}}}{x^{1}}\\= x^{ \frac{-3}{4} - 1 }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{3}{4} - (\frac{-3}{2}) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-1}{4} - (\frac{-4}{5}) }= a^{\frac{11}{20}}\\=\sqrt[20]{ a^{11} }\\---------------\)