Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{6} - (\frac{-1}{2}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-3}{5}}}\\= y^{ -1 - (\frac{-3}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-1}{3} - \frac{2}{5} }= q^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ q^{11} }}=\frac{1}{\sqrt[15]{ q^{11} }}. \color{purple}{\frac{\sqrt[15]{ q^{4} }}{\sqrt[15]{ q^{4} }}} \\=\frac{\sqrt[15]{ q^{4} }}{q}\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{-1}{4}}}\\= q^{ 1 - (\frac{-1}{4}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{6}) }= q^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ q^{7} }}=\frac{1}{\sqrt[30]{ q^{7} }}. \color{purple}{\frac{\sqrt[30]{ q^{23} }}{\sqrt[30]{ q^{23} }}} \\=\frac{\sqrt[30]{ q^{23} }}{|q|}\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{-1}{3}}}\\= q^{ -1 - (\frac{-1}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
7. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{5} - (\frac{-1}{3}) }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{4}{3}}}\\= a^{ -1 - \frac{4}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{2} - (\frac{-3}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
11. \(\dfrac{q^{2}}{q^{\frac{1}{5}}}\\= q^{ 2 - \frac{1}{5} }= q^{\frac{9}{5}}\\=\sqrt[5]{ q^{9} }=q.\sqrt[5]{ q^{4} }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{2}) }= y^{2}\\\\---------------\)