Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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