Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{2}{3}}}\\= x^{ -1 - \frac{2}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
2. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-5}{4} - \frac{1}{6} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{2}{5} - \frac{1}{3} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-3}{2}) }= x^{1}\\\\---------------\)
5. \(\dfrac{y^{\frac{-5}{3}}}{y^{1}}\\= y^{ \frac{-5}{3} - 1 }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
6. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{4} - (\frac{-5}{4}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
7. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{3} - \frac{5}{4} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-2}{3} - \frac{5}{4} }= q^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{11} }}=\frac{1}{|q|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-5}{4} - \frac{4}{5} }= a^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ a^{41} }}\\=\frac{1}{|a^{2}|.\sqrt[20]{ a }}=\frac{1}{|a^{2}|.\sqrt[20]{ a }} \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a^{3}|}\\---------------\)
10. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{1}{4} - (\frac{-3}{2}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
11. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-3}{2} - (\frac{-3}{5}) }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
12. \(\dfrac{x^{\frac{2}{3}}}{x^{-2}}\\= x^{ \frac{2}{3} - (-2) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)