Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{5}{4} - \frac{1}{2} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{3}{4}}}\\= a^{ \frac{3}{4} - \frac{3}{4} }= a^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{6} - (\frac{-1}{5}) }= y^{\frac{11}{30}}\\=\sqrt[30]{ y^{11} }\\---------------\)
4. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{4}{5} - (\frac{-2}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-5}{3}}}\\= x^{ -1 - (\frac{-5}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
6. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-3}{2} - \frac{1}{3} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{1}}\\= a^{ \frac{1}{2} - 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{4}{3}}}\\= a^{ \frac{5}{6} - \frac{4}{3} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-4}{3} - (\frac{-3}{4}) }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
11. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{4}{5} - \frac{5}{3} }= q^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ q^{13} }}=\frac{1}{\sqrt[15]{ q^{13} }}. \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{2} - \frac{1}{5} }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)