Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{2}{3}}}{y^{-1}}\\= y^{ \frac{2}{3} - (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{6}}}\\= a^{ \frac{1}{3} - \frac{1}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-4}{5}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
4. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{1}{6}}}\\= q^{ \frac{2}{5} - \frac{1}{6} }= q^{\frac{7}{30}}\\=\sqrt[30]{ q^{7} }\\---------------\)
5. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{4}{3} - \frac{1}{3} }= a^{1}\\\\---------------\)
6. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{5} - (\frac{-2}{5}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
8. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{3} - (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{2} - (\frac{-1}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{1}{3} - (\frac{-5}{6}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)