Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{2}}{q^{\frac{3}{4}}}\\= q^{ 2 - \frac{3}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-5}{4} - \frac{3}{4} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{5}{6}}}\\= a^{ \frac{1}{6} - \frac{5}{6} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{2}}}{q^{-1}}\\= q^{ \frac{-1}{2} - (-1) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
5. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-3}{4} - (\frac{-5}{2}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
6. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{4} - \frac{1}{3} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
7. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-5}{6} - (\frac{-3}{5}) }= y^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ y^{7} }}=\frac{1}{\sqrt[30]{ y^{7} }}. \color{purple}{\frac{\sqrt[30]{ y^{23} }}{\sqrt[30]{ y^{23} }}} \\=\frac{\sqrt[30]{ y^{23} }}{|y|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{3}{2} - (\frac{-4}{3}) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{5} - (\frac{-2}{5}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{2}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
12. \(\dfrac{x^{1}}{x^{-1}}\\= x^{ 1 - (-1) }= x^{2}\\\\---------------\)