Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{2}{3} - (\frac{-5}{6}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{5}{3} - \frac{2}{5} }= y^{\frac{19}{15}}\\=\sqrt[15]{ y^{19} }=y.\sqrt[15]{ y^{4} }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{6} - (\frac{-3}{4}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\\= y^{ 1 - \frac{1}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{1}{2} - (\frac{-5}{4}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{6} - (\frac{-5}{2}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
9. \(\dfrac{x^{-2}}{x^{\frac{1}{3}}}\\= x^{ -2 - \frac{1}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-1}{6} - \frac{5}{2} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
11. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{5}{3} - \frac{4}{5} }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{5}{3}}}\\= y^{ 1 - \frac{5}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)