Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{4}{3} - \frac{1}{5} }= a^{\frac{17}{15}}\\=\sqrt[15]{ a^{17} }=a.\sqrt[15]{ a^{2} }\\---------------\)
2. \(\dfrac{a^{\frac{-4}{3}}}{a^{-2}}\\= a^{ \frac{-4}{3} - (-2) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{1}}\\= q^{ \frac{2}{5} - 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
4. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-5}{3} - \frac{3}{2} }= a^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ a^{19} }}\\=\frac{1}{|a^{3}|.\sqrt[6]{ a }}=\frac{1}{|a^{3}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{4}|}\\---------------\)
5. \(\dfrac{a^{2}}{a^{-1}}\\= a^{ 2 - (-1) }= a^{3}\\\\---------------\)
6. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{4} - (\frac{-5}{4}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
7. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{3} - \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
8. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-3}{5} - (\frac{-5}{6}) }= a^{\frac{7}{30}}\\=\sqrt[30]{ a^{7} }\\---------------\)
9. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
10. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-3}{5} - \frac{1}{4} }= a^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ a^{17} }}=\frac{1}{\sqrt[20]{ a^{17} }}. \color{purple}{\frac{\sqrt[20]{ a^{3} }}{\sqrt[20]{ a^{3} }}} \\=\frac{\sqrt[20]{ a^{3} }}{|a|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{2} - (\frac{-4}{3}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
12. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{3}{5}}}\\= y^{ \frac{2}{5} - \frac{3}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)