Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{4} - (\frac{-5}{3}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
2. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-2}{5} - (\frac{-2}{3}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{4}}}{q^{1}}\\= q^{ \frac{-1}{4} - 1 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{2} - (\frac{-2}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
5. \(\dfrac{x^{\frac{-4}{3}}}{x^{-1}}\\= x^{ \frac{-4}{3} - (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\dfrac{q^{\frac{5}{2}}}{q^{1}}\\= q^{ \frac{5}{2} - 1 }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{-1}{4}}}\\= x^{ -1 - (\frac{-1}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{6} - \frac{4}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{3}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{2}{3} - (\frac{-5}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{3} - \frac{5}{3} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{3} - (\frac{-1}{5}) }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)