Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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