Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
2. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-4}{3} - (\frac{-1}{5}) }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-1}{5} - \frac{4}{3} }= y^{\frac{-23}{15}}\\=\frac{1}{\sqrt[15]{ y^{23} }}\\=\frac{1}{y.\sqrt[15]{ y^{8} }}=\frac{1}{y.\sqrt[15]{ y^{8} }} \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{4}}}\\= y^{ \frac{4}{5} - \frac{1}{4} }= y^{\frac{11}{20}}\\=\sqrt[20]{ y^{11} }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-1}{6} - \frac{3}{5} }= y^{\frac{-23}{30}}\\=\frac{1}{\sqrt[30]{ y^{23} }}=\frac{1}{\sqrt[30]{ y^{23} }}. \color{purple}{\frac{\sqrt[30]{ y^{7} }}{\sqrt[30]{ y^{7} }}} \\=\frac{\sqrt[30]{ y^{7} }}{|y|}\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{2} - \frac{3}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\dfrac{x^{\frac{-5}{3}}}{x^{-1}}\\= x^{ \frac{-5}{3} - (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
8. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{2}{3} - (\frac{-3}{4}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
9. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
10. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-2}{3}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{4}{5}}}\\= y^{ -1 - \frac{4}{5} }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{4}{5}}}\\= x^{ \frac{3}{4} - \frac{4}{5} }= x^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ x }}=\frac{1}{\sqrt[20]{ x }}. \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x|}\\---------------\)