Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{5} - \frac{4}{3} }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-5}{2}}}\\= y^{ -1 - (\frac{-5}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
3. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-5}{2} - \frac{5}{6} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\\= y^{ \frac{-1}{2} - 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
6. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{-3}{2}}}{q^{-1}}\\= q^{ \frac{-3}{2} - (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{6}}}\\= q^{ \frac{3}{5} - \frac{1}{6} }= q^{\frac{13}{30}}\\=\sqrt[30]{ q^{13} }\\---------------\)
9. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{2}{3} - \frac{5}{6} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
10. \(\dfrac{x^{\frac{-3}{2}}}{x^{2}}\\= x^{ \frac{-3}{2} - 2 }= x^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ x^{7} } }\\=\frac{1}{|x^{3}|. \sqrt{ x } }=\frac{1}{|x^{3}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{4}|}\\---------------\)
11. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-2}{3} - \frac{3}{5} }= x^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ x^{19} }}\\=\frac{1}{x.\sqrt[15]{ x^{4} }}=\frac{1}{x.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{5}{3} - (\frac{-5}{6}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)