Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{4} - (\frac{-5}{4}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
2. \(\dfrac{q^{\frac{4}{5}}}{q^{-1}}\\= q^{ \frac{4}{5} - (-1) }= q^{\frac{9}{5}}\\=\sqrt[5]{ q^{9} }=q.\sqrt[5]{ q^{4} }\\---------------\)
3. \(\dfrac{y^{-2}}{y^{\frac{4}{3}}}\\= y^{ -2 - \frac{4}{3} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-5}{4} - (\frac{-1}{4}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-1}{5} - \frac{5}{6} }= x^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ x^{31} }}\\=\frac{1}{|x|.\sqrt[30]{ x }}=\frac{1}{|x|.\sqrt[30]{ x }} \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{1}{2} - (\frac{-2}{5}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
8. \(\dfrac{q^{\frac{3}{2}}}{q^{-2}}\\= q^{ \frac{3}{2} - (-2) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{-1}{5}}}\\= y^{ -1 - (\frac{-1}{5}) }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
10. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{5}{3} - (\frac{-5}{2}) }= x^{\frac{25}{6}}\\=\sqrt[6]{ x^{25} }=|x^{4}|.\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{y^{\frac{-4}{5}}}{y^{-1}}\\= y^{ \frac{-4}{5} - (-1) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-5}{2}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)