Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{4}{5} - \frac{2}{3} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{4}}}{a^{-1}}\\= a^{ \frac{1}{4} - (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{x^{\frac{4}{3}}}{x^{-1}}\\= x^{ \frac{4}{3} - (-1) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{3} - (\frac{-1}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-1}{6} - (\frac{-3}{2}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{y^{-2}}{y^{1}}\\= y^{ -2 - 1 }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{5}{3} - \frac{5}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-4}{3} - (\frac{-5}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{4}{5} - (\frac{-1}{2}) }= x^{\frac{13}{10}}\\=\sqrt[10]{ x^{13} }=|x|.\sqrt[10]{ x^{3} }\\---------------\)
10. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{4}{3} - (\frac{-3}{5}) }= y^{\frac{29}{15}}\\=\sqrt[15]{ y^{29} }=y.\sqrt[15]{ y^{14} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{2} - \frac{1}{2} }= a^{0}\\=1\\---------------\)
12. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{5}{4} - \frac{1}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)