Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-5}{3} - \frac{1}{6} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{2}{3} - \frac{5}{4} }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{2} - \frac{3}{5} }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
4. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{2}{3} - \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
5. \(\dfrac{x^{\frac{5}{6}}}{x^{-1}}\\= x^{ \frac{5}{6} - (-1) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
6. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-4}{3} - (\frac{-5}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{1}{3}}}\\= q^{ -1 - \frac{1}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
8. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{3}{2} - \frac{2}{3} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-4}{5} - \frac{2}{3} }= y^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ y^{22} }}\\=\frac{1}{y.\sqrt[15]{ y^{7} }}=\frac{1}{y.\sqrt[15]{ y^{7} }} \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{2}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{1}{2} - \frac{4}{5} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
12. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-4}{3} - (\frac{-1}{4}) }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)