Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{4}}}{q^{-1}}\\= q^{ \frac{-5}{4} - (-1) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
2. \(\dfrac{x^{1}}{x^{\frac{-4}{5}}}\\= x^{ 1 - (\frac{-4}{5}) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{2} - \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{5}{6}}}\\= y^{ \frac{5}{6} - \frac{5}{6} }= y^{0}\\=1\\---------------\)
5. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{x^{\frac{-2}{3}}}{x^{-1}}\\= x^{ \frac{-2}{3} - (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-3}{2} - (\frac{-1}{6}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{3}{5} - \frac{5}{4} }= x^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ x^{13} }}=\frac{1}{\sqrt[20]{ x^{13} }}. \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-2}{3}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
10. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-2}{3} - (\frac{-5}{2}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{6}) }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\\= y^{ \frac{1}{3} - (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)