Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-5}{2} - (\frac{-5}{3}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{-1}}\\= a^{ \frac{2}{3} - (-1) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{3}{4} - (\frac{-4}{5}) }= x^{\frac{31}{20}}\\=\sqrt[20]{ x^{31} }=|x|.\sqrt[20]{ x^{11} }\\---------------\)
4. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-2}{5} - (\frac{-5}{6}) }= a^{\frac{13}{30}}\\=\sqrt[30]{ a^{13} }\\---------------\)
5. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{5}{2}}}\\= a^{ \frac{5}{2} - \frac{5}{2} }= a^{0}\\=1\\---------------\)
6. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{5}) }= x^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ x^{7} }}=\frac{1}{\sqrt[15]{ x^{7} }}. \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x}\\---------------\)
7. \(\dfrac{x^{\frac{5}{6}}}{x^{2}}\\= x^{ \frac{5}{6} - 2 }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{2} - (\frac{-2}{3}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
9. \(\dfrac{y^{\frac{-5}{6}}}{y^{1}}\\= y^{ \frac{-5}{6} - 1 }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{5}{6}}}\\= a^{ \frac{4}{5} - \frac{5}{6} }= a^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ a }}=\frac{1}{\sqrt[30]{ a }}. \color{purple}{\frac{\sqrt[30]{ a^{29} }}{\sqrt[30]{ a^{29} }}} \\=\frac{\sqrt[30]{ a^{29} }}{|a|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{5} - (\frac{-2}{3}) }= a^{\frac{13}{15}}\\=\sqrt[15]{ a^{13} }\\---------------\)
12. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{3} - \frac{1}{2} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)