Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{5}{3}}}\\= a^{ 1 - \frac{5}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
2. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{3} - \frac{1}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
4. \(\dfrac{y^{2}}{y^{\frac{-1}{3}}}\\= y^{ 2 - (\frac{-1}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{5} - (\frac{-1}{3}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{3}{5} - (\frac{-1}{4}) }= q^{\frac{17}{20}}\\=\sqrt[20]{ q^{17} }\\---------------\)
7. \(\dfrac{a^{\frac{-5}{6}}}{a^{1}}\\= a^{ \frac{-5}{6} - 1 }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
8. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{3}{5} - (\frac{-4}{3}) }= x^{\frac{29}{15}}\\=\sqrt[15]{ x^{29} }=x.\sqrt[15]{ x^{14} }\\---------------\)
9. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{5}{3} - (\frac{-5}{2}) }= a^{\frac{25}{6}}\\=\sqrt[6]{ a^{25} }=|a^{4}|.\sqrt[6]{ a }\\---------------\)
11. \(\dfrac{q^{\frac{3}{2}}}{q^{-1}}\\= q^{ \frac{3}{2} - (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
12. \(\dfrac{a^{-2}}{a^{\frac{3}{2}}}\\= a^{ -2 - \frac{3}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)