Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{5}}}{q^{1}}\\= q^{ \frac{2}{5} - 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-5}{3} - \frac{4}{5} }= q^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ q^{37} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }}=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{3}}\\---------------\)
3. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{6} - (\frac{-2}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{3} - \frac{1}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
5. \(\dfrac{x^{1}}{x^{\frac{-5}{4}}}\\= x^{ 1 - (\frac{-5}{4}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
6. \(\dfrac{y^{\frac{5}{4}}}{y^{-1}}\\= y^{ \frac{5}{4} - (-1) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{4} - \frac{3}{5} }= x^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ x^{7} }}=\frac{1}{\sqrt[20]{ x^{7} }}. \color{purple}{\frac{\sqrt[20]{ x^{13} }}{\sqrt[20]{ x^{13} }}} \\=\frac{\sqrt[20]{ x^{13} }}{|x|}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
9. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{2}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
10. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{6} - \frac{2}{3} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
11. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{5}{2} - \frac{5}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
12. \(\dfrac{q^{\frac{5}{2}}}{q^{-1}}\\= q^{ \frac{5}{2} - (-1) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)