Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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