Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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