Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-2}}{q^{\frac{-5}{6}}}\\= q^{ -2 - (\frac{-5}{6}) }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{3}{5} - \frac{1}{6} }= y^{\frac{13}{30}}\\=\sqrt[30]{ y^{13} }\\---------------\)
3. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{1}{5} - (\frac{-5}{6}) }= y^{\frac{31}{30}}\\=\sqrt[30]{ y^{31} }=|y|.\sqrt[30]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{2} - \frac{2}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{4} - \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-2}{3}) }= y^{\frac{7}{15}}\\=\sqrt[15]{ y^{7} }\\---------------\)
7. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-5}{3}) }= y^{1}\\\\---------------\)
9. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{2} - (\frac{-1}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{5}{3} - \frac{1}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{2} - \frac{5}{6} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)