Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{4}{5}}}{a^{1}}\\= a^{ \frac{4}{5} - 1 }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{1}{6}}}\\= y^{ 1 - \frac{1}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{4} - \frac{4}{5} }= x^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ x^{21} }}\\=\frac{1}{|x|.\sqrt[20]{ x }}=\frac{1}{|x|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{4}{3}}}{a^{-1}}\\= a^{ \frac{4}{3} - (-1) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{5}{6}}}\\= a^{ 1 - \frac{5}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-5}{2} - \frac{3}{5} }= a^{\frac{-31}{10}}\\=\frac{1}{\sqrt[10]{ a^{31} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a }}=\frac{1}{|a^{3}|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{4}|}\\---------------\)
7. \(\dfrac{y^{\frac{3}{4}}}{y^{-1}}\\= y^{ \frac{3}{4} - (-1) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
8. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-3}{2} - (\frac{-5}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{5}{2} - (\frac{-3}{5}) }= y^{\frac{31}{10}}\\=\sqrt[10]{ y^{31} }=|y^{3}|.\sqrt[10]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{1}{6}}}{y^{1}}\\= y^{ \frac{1}{6} - 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-4}{5}) }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-5}{3} - \frac{2}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)