Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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