Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{3} - (\frac{-1}{2}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{y^{2}}{y^{\frac{-1}{2}}}\\= y^{ 2 - (\frac{-1}{2}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-1}{2} - \frac{3}{5} }= a^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[10]{ a }}=\frac{1}{|a|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{2} - \frac{2}{3} }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-4}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{2}{3} - \frac{2}{3} }= a^{0}\\=1\\---------------\)
7. \(\dfrac{a^{2}}{a^{-1}}\\= a^{ 2 - (-1) }= a^{3}\\\\---------------\)
8. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{5}{6} - (\frac{-3}{4}) }= q^{\frac{19}{12}}\\=\sqrt[12]{ q^{19} }=|q|.\sqrt[12]{ q^{7} }\\---------------\)
9. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{5}{3} - (\frac{-3}{4}) }= x^{\frac{29}{12}}\\=\sqrt[12]{ x^{29} }=|x^{2}|.\sqrt[12]{ x^{5} }\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{-5}{6}}}\\= x^{ 1 - (\frac{-5}{6}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{2}{3} - \frac{4}{5} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)