Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-4}{5} - \frac{3}{2} }= q^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ q^{23} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{3}|}\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{-3}{2}}}\\= q^{ -1 - (\frac{-3}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{2}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{2} - \frac{2}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{5}{6}}}\\= a^{ \frac{5}{6} - \frac{5}{6} }= a^{0}\\=1\\---------------\)
7. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-4}{5} - \frac{1}{4} }= q^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ q^{21} }}\\=\frac{1}{|q|.\sqrt[20]{ q }}=\frac{1}{|q|.\sqrt[20]{ q }} \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{6} - \frac{1}{6} }= q^{0}\\=1\\---------------\)
9. \(\dfrac{q^{\frac{-3}{4}}}{q^{-1}}\\= q^{ \frac{-3}{4} - (-1) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{2} - (\frac{-5}{2}) }= y^{3}\\\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{2} - \frac{5}{6} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{-4}{5}}}\\= x^{ -1 - (\frac{-4}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)