Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{5}{3} - \frac{1}{2} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{5}{2} - (\frac{-4}{5}) }= q^{\frac{33}{10}}\\=\sqrt[10]{ q^{33} }=|q^{3}|.\sqrt[10]{ q^{3} }\\---------------\)
3. \(\dfrac{q^{2}}{q^{1}}\\= q^{ 2 - 1 }= q^{1}\\\\---------------\)
4. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{4} - (\frac{-5}{2}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
5. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-2}{5} - \frac{1}{3} }= x^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ x^{11} }}=\frac{1}{\sqrt[15]{ x^{11} }}. \color{purple}{\frac{\sqrt[15]{ x^{4} }}{\sqrt[15]{ x^{4} }}} \\=\frac{\sqrt[15]{ x^{4} }}{x}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
7. \(\dfrac{a^{-2}}{a^{\frac{3}{2}}}\\= a^{ -2 - \frac{3}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
8. \(\dfrac{a^{2}}{a^{\frac{1}{5}}}\\= a^{ 2 - \frac{1}{5} }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{5}{2}}}\\= a^{ -1 - \frac{5}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{5} - (\frac{-3}{2}) }= y^{\frac{13}{10}}\\=\sqrt[10]{ y^{13} }=|y|.\sqrt[10]{ y^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{4}}}\\= q^{ \frac{5}{4} - \frac{1}{4} }= q^{1}\\\\---------------\)
12. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{2} - \frac{1}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)