Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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