Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{6}}}{x^{-1}}\\= x^{ \frac{5}{6} - (-1) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{5} - (\frac{-5}{2}) }= x^{\frac{23}{10}}\\=\sqrt[10]{ x^{23} }=|x^{2}|.\sqrt[10]{ x^{3} }\\---------------\)
3. \(\dfrac{a^{\frac{-3}{5}}}{a^{-2}}\\= a^{ \frac{-3}{5} - (-2) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{-3}{4}}}\\= a^{ 1 - (\frac{-3}{4}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
5. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{5} - (\frac{-1}{2}) }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)
6. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-2}{5} - \frac{5}{6} }= a^{\frac{-37}{30}}\\=\frac{1}{\sqrt[30]{ a^{37} }}\\=\frac{1}{|a|.\sqrt[30]{ a^{7} }}=\frac{1}{|a|.\sqrt[30]{ a^{7} }} \color{purple}{\frac{\sqrt[30]{ a^{23} }}{\sqrt[30]{ a^{23} }}} \\=\frac{\sqrt[30]{ a^{23} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{4} - (\frac{-5}{4}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
8. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{5} - (\frac{-4}{3}) }= q^{\frac{23}{15}}\\=\sqrt[15]{ q^{23} }=q.\sqrt[15]{ q^{8} }\\---------------\)
9. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{6} - \frac{1}{2} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-2}{5} - (\frac{-5}{3}) }= y^{\frac{19}{15}}\\=\sqrt[15]{ y^{19} }=y.\sqrt[15]{ y^{4} }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-1}{6} - (\frac{-5}{4}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{-2}{3}}}\\= x^{ 1 - (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)