Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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