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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{2}}{q^{\frac{-5}{6}}}\\= q^{ 2 - (\frac{-5}{6}) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{-3}{2}}}\\= a^{ 1 - (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
3. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{2} - \frac{1}{2} }= q^{0}\\=1\\---------------\)
4. \(\dfrac{y^{\frac{5}{6}}}{y^{2}}\\= y^{ \frac{5}{6} - 2 }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-5}{2} - (\frac{-3}{2}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-1}{4} - (\frac{-3}{2}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
7. \(\dfrac{x^{2}}{x^{\frac{-5}{2}}}\\= x^{ 2 - (\frac{-5}{2}) }= x^{\frac{9}{2}}\\= \sqrt{ x^{9} } =|x^{4}|. \sqrt{ x } \\---------------\)
8. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{3}{2} - (\frac{-3}{2}) }= a^{3}\\\\---------------\)
9. \(\dfrac{q^{\frac{5}{3}}}{q^{1}}\\= q^{ \frac{5}{3} - 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-4}{3} - (\frac{-5}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
11. \(\dfrac{x^{2}}{x^{\frac{5}{6}}}\\= x^{ 2 - \frac{5}{6} }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
12. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{2}{5} - (\frac{-2}{3}) }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)