Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{5}{3} - \frac{1}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{x^{1}}{x^{\frac{-3}{4}}}\\= x^{ 1 - (\frac{-3}{4}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
3. \(\dfrac{x^{\frac{2}{3}}}{x^{-1}}\\= x^{ \frac{2}{3} - (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{6}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{2} - \frac{2}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{2}{5}}}\\= y^{ \frac{3}{5} - \frac{2}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{5}) }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
8. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-4}{3} - (\frac{-4}{5}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
9. \(\dfrac{a^{\frac{4}{5}}}{a^{1}}\\= a^{ \frac{4}{5} - 1 }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
10. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{3} - \frac{2}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{-2}}\\= q^{ -1 - (-2) }= q^{1}\\\\---------------\)
12. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{4}{5} - \frac{5}{2} }= q^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{7} }}=\frac{1}{|q|.\sqrt[10]{ q^{7} }} \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q^{2}|}\\---------------\)