Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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