Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{2} - \frac{5}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{2} - \frac{4}{5} }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-5}{6} - \frac{5}{2} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{5}}}{a^{-2}}\\= a^{ \frac{-3}{5} - (-2) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
5. \(\dfrac{a^{\frac{1}{3}}}{a^{-1}}\\= a^{ \frac{1}{3} - (-1) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{a^{\frac{2}{3}}}{a^{-1}}\\= a^{ \frac{2}{3} - (-1) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{2}{3} - (\frac{-1}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
8. \(\dfrac{x^{2}}{x^{1}}\\= x^{ 2 - 1 }= x^{1}\\\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\dfrac{x^{\frac{-3}{5}}}{x^{-1}}\\= x^{ \frac{-3}{5} - (-1) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{2}{5} - \frac{5}{6} }= y^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ y^{13} }}=\frac{1}{\sqrt[30]{ y^{13} }}. \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{3}{5} - \frac{3}{2} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)