Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{6}}}{q^{-1}}\\= q^{ \frac{-1}{6} - (-1) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
2. \(\dfrac{x^{1}}{x^{\frac{-1}{4}}}\\= x^{ 1 - (\frac{-1}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
3. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{5}{4} - (\frac{-1}{4}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
4. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{5} - \frac{5}{3} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{1}{4}}}\\= a^{ \frac{4}{5} - \frac{1}{4} }= a^{\frac{11}{20}}\\=\sqrt[20]{ a^{11} }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-5}{6} - \frac{5}{2} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
7. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{4} - \frac{1}{2} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
8. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-5}{3} - \frac{4}{3} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
9. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-4}{3} - \frac{1}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{4}}}\\= q^{ \frac{5}{6} - \frac{5}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{3} - \frac{2}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{3}{2} - \frac{5}{6} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)