Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-4}{3} - \frac{1}{2} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{5}}}{y^{-1}}\\= y^{ \frac{1}{5} - (-1) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
3. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{1}{3} - (\frac{-3}{4}) }= y^{\frac{13}{12}}\\=\sqrt[12]{ y^{13} }=|y|.\sqrt[12]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{5}{2} - (\frac{-2}{5}) }= x^{\frac{29}{10}}\\=\sqrt[10]{ x^{29} }=|x^{2}|.\sqrt[10]{ x^{9} }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-3}{2} - \frac{4}{3} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{2}}}\\= a^{ \frac{1}{2} - \frac{5}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{2}{3} - \frac{5}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-1}{3} - \frac{4}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-4}{3} - \frac{3}{2} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)
11. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-5}{4} - (\frac{-2}{3}) }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
12. \(\dfrac{y^{\frac{-3}{4}}}{y^{-1}}\\= y^{ \frac{-3}{4} - (-1) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)