Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{4}{5} - \frac{1}{3} }= a^{\frac{7}{15}}\\=\sqrt[15]{ a^{7} }\\---------------\)
2. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{1}{3} - \frac{3}{4} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{2} - \frac{1}{2} }= a^{0}\\=1\\---------------\)
4. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{4}{3} - (\frac{-4}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{1}{4} - (\frac{-1}{5}) }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{2}{3} - (\frac{-1}{3}) }= x^{1}\\\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{-2}}\\= q^{ \frac{1}{2} - (-2) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
9. \(\dfrac{y^{2}}{y^{2}}\\= y^{ 2 - 2 }= y^{0}\\=1\\---------------\)
10. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{2}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
11. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
12. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{2}{5} - (\frac{-3}{5}) }= a^{1}\\\\---------------\)