Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{2} - (\frac{-3}{5}) }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
2. \(\dfrac{q^{\frac{1}{5}}}{q^{-1}}\\= q^{ \frac{1}{5} - (-1) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
3. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{5}{3} - (\frac{-4}{3}) }= y^{3}\\\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-2}{3} - \frac{3}{5} }= y^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ y^{19} }}\\=\frac{1}{y.\sqrt[15]{ y^{4} }}=\frac{1}{y.\sqrt[15]{ y^{4} }} \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{1}{3} - (\frac{-5}{2}) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
6. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{3}{5} - \frac{1}{2} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
7. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-1}{5} - \frac{5}{2} }= x^{\frac{-27}{10}}\\=\frac{1}{\sqrt[10]{ x^{27} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{7} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{7} }} \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x^{3}|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{1}{3} - (\frac{-4}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
10. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{3}{2} - (\frac{-1}{3}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
11. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-1}{6} - \frac{4}{5} }= q^{\frac{-29}{30}}\\=\frac{1}{\sqrt[30]{ q^{29} }}=\frac{1}{\sqrt[30]{ q^{29} }}. \color{purple}{\frac{\sqrt[30]{ q }}{\sqrt[30]{ q }}} \\=\frac{\sqrt[30]{ q }}{|q|}\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{3}{4}}}\\= x^{ -1 - \frac{3}{4} }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)