Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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