Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{4}}}{x^{-2}}\\= x^{ \frac{-5}{4} - (-2) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
3. \(\dfrac{x^{\frac{5}{3}}}{x^{1}}\\= x^{ \frac{5}{3} - 1 }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
4. \(\dfrac{a^{-2}}{a^{\frac{5}{2}}}\\= a^{ -2 - \frac{5}{2} }= a^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ a^{9} } }\\=\frac{1}{|a^{4}|. \sqrt{ a } }=\frac{1}{|a^{4}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{5}|}\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-2}{3} - \frac{5}{4} }= a^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{11} }}=\frac{1}{|a|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-5}{6} - (\frac{-3}{4}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{3}{5}}}\\= a^{ -1 - \frac{3}{5} }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{3}}}\\= x^{ \frac{3}{5} - \frac{5}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{4}}}\\= y^{ \frac{4}{5} - \frac{1}{4} }= y^{\frac{11}{20}}\\=\sqrt[20]{ y^{11} }\\---------------\)
10. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-4}{5} - \frac{5}{2} }= q^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ q^{33} }}\\=\frac{1}{|q^{3}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{3}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{4}|}\\---------------\)
11. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-3}{4} - (\frac{-4}{5}) }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{2}{3} - \frac{3}{2} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)