Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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