Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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