Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{-4}{3}}}\\= x^{ -1 - (\frac{-4}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
2. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-4}{5} - \frac{5}{3} }= a^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ a^{37} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a^{7} }}=\frac{1}{a^{2}.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{3}}\\---------------\)
3. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-3}{4} - \frac{3}{5} }= y^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ y^{27} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{7} }}=\frac{1}{|y|.\sqrt[20]{ y^{7} }} \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{4}{5}}}\\= a^{ \frac{5}{6} - \frac{4}{5} }= a^{\frac{1}{30}}\\=\sqrt[30]{ a }\\---------------\)
5. \(\dfrac{y^{2}}{y^{-1}}\\= y^{ 2 - (-1) }= y^{3}\\\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{2}{5}}}\\= x^{ 1 - \frac{2}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
7. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{5} - (\frac{-4}{5}) }= q^{1}\\\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{1}}\\= q^{ \frac{4}{5} - 1 }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
9. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{2}{5}}}\\= y^{ \frac{3}{5} - \frac{2}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
10. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{5} - \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{x^{-2}}{x^{\frac{-1}{2}}}\\= x^{ -2 - (\frac{-1}{2}) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)