Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{3}{5} - (\frac{-2}{5}) }= x^{1}\\\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{2}{3} - (\frac{-4}{5}) }= x^{\frac{22}{15}}\\=\sqrt[15]{ x^{22} }=x.\sqrt[15]{ x^{7} }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{-4}{3}}}\\= q^{ -1 - (\frac{-4}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{-3}{2}}}{a^{-2}}\\= a^{ \frac{-3}{2} - (-2) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
5. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{1}{6} - (\frac{-1}{4}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{1}{6}}}\\= y^{ 1 - \frac{1}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{2} - (\frac{-1}{2}) }= q^{1}\\\\---------------\)
8. \(\dfrac{y^{2}}{y^{\frac{-1}{3}}}\\= y^{ 2 - (\frac{-1}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-4}{3} - (\frac{-2}{5}) }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-1}{2} - \frac{1}{6} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{2} - (\frac{-5}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)