Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{2}}}{y^{-1}}\\= y^{ \frac{5}{2} - (-1) }= y^{\frac{7}{2}}\\= \sqrt{ y^{7} } =|y^{3}|. \sqrt{ y } \\---------------\)
2. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{4}{3} - (\frac{-1}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{5}{2}}}\\= x^{ 1 - \frac{5}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{2}{5} - (\frac{-1}{6}) }= y^{\frac{17}{30}}\\=\sqrt[30]{ y^{17} }\\---------------\)
6. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-5}{2} - \frac{1}{2} }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
8. \(\dfrac{a^{\frac{-5}{6}}}{a^{1}}\\= a^{ \frac{-5}{6} - 1 }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{5} - \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
10. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{2}{5} - \frac{1}{2} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
11. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-5}{3} - \frac{5}{6} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-5}{4} - (\frac{-3}{5}) }= y^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ y^{13} }}=\frac{1}{\sqrt[20]{ y^{13} }}. \color{purple}{\frac{\sqrt[20]{ y^{7} }}{\sqrt[20]{ y^{7} }}} \\=\frac{\sqrt[20]{ y^{7} }}{|y|}\\---------------\)