Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{5}}}\\= a^{ \frac{5}{4} - \frac{1}{5} }= a^{\frac{21}{20}}\\=\sqrt[20]{ a^{21} }=|a|.\sqrt[20]{ a }\\---------------\)
3. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-3}{4} - (\frac{-4}{5}) }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{2} - (\frac{-4}{5}) }= y^{\frac{13}{10}}\\=\sqrt[10]{ y^{13} }=|y|.\sqrt[10]{ y^{3} }\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{1}{2} - (\frac{-5}{2}) }= x^{3}\\\\---------------\)
6. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{2} - \frac{1}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{3}{2}}}{q^{-1}}\\= q^{ \frac{3}{2} - (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
9. \(\dfrac{a^{\frac{-4}{5}}}{a^{-1}}\\= a^{ \frac{-4}{5} - (-1) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{3} - \frac{5}{4} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)