Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{3} - \frac{1}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{2}{5}}}\\= q^{ -1 - \frac{2}{5} }= q^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ q^{7} }}\\=\frac{1}{q.\sqrt[5]{ q^{2} }}=\frac{1}{q.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{4}}}{x^{-1}}\\= x^{ \frac{-5}{4} - (-1) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{4}{3} - (\frac{-2}{3}) }= y^{2}\\\\---------------\)
5. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{2} - \frac{1}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{3}{5} - (\frac{-5}{3}) }= x^{\frac{34}{15}}\\=\sqrt[15]{ x^{34} }=x^{2}.\sqrt[15]{ x^{4} }\\---------------\)
7. \(\dfrac{x^{-2}}{x^{\frac{1}{3}}}\\= x^{ -2 - \frac{1}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
8. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{5}{2} - (\frac{-5}{2}) }= x^{5}\\\\---------------\)
9. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
11. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-2}{3} - \frac{3}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
12. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{3}{5} - (\frac{-2}{3}) }= a^{\frac{19}{15}}\\=\sqrt[15]{ a^{19} }=a.\sqrt[15]{ a^{4} }\\---------------\)