Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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