Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-4}{3} - (\frac{-4}{3}) }= x^{0}\\=1\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-1}{3} - \frac{3}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{-1}}\\= q^{ \frac{-1}{2} - (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
4. \(\dfrac{a^{-1}}{a^{-2}}\\= a^{ -1 - (-2) }= a^{1}\\\\---------------\)
5. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-5}{3} - \frac{2}{5} }= q^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ q^{31} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q }}=\frac{1}{q^{2}.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{3}}\\---------------\)
6. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{5} - \frac{1}{4} }= q^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ q }}=\frac{1}{\sqrt[20]{ q }}. \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q|}\\---------------\)
7. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-3}{4} - \frac{5}{2} }= x^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ x^{13} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x }}=\frac{1}{|x^{3}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{4}|}\\---------------\)
8. \(\dfrac{a^{-1}}{a^{\frac{5}{4}}}\\= a^{ -1 - \frac{5}{4} }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
9. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-2}{5} - (\frac{-4}{5}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{-5}{2}}}\\= x^{ 1 - (\frac{-5}{2}) }= x^{\frac{7}{2}}\\= \sqrt{ x^{7} } =|x^{3}|. \sqrt{ x } \\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{1}{2} - (\frac{-1}{5}) }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{-4}{5}}}\\= y^{ 1 - (\frac{-4}{5}) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)