Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{2}{5}}}\\= y^{ 1 - \frac{2}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
3. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{3}{5} - (\frac{-1}{3}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
4. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{3}{4} - (\frac{-5}{2}) }= a^{\frac{13}{4}}\\=\sqrt[4]{ a^{13} }=|a^{3}|.\sqrt[4]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-3}{2} - (\frac{-4}{5}) }= a^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ a^{7} }}=\frac{1}{\sqrt[10]{ a^{7} }}. \color{purple}{\frac{\sqrt[10]{ a^{3} }}{\sqrt[10]{ a^{3} }}} \\=\frac{\sqrt[10]{ a^{3} }}{|a|}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{5}) }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)
7. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{3}{5} - \frac{3}{2} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
8. \(\dfrac{a^{-2}}{a^{\frac{5}{6}}}\\= a^{ -2 - \frac{5}{6} }= a^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ a^{17} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a^{5} }}=\frac{1}{|a^{2}|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{3}|}\\---------------\)
9. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{2}{5} - (\frac{-1}{4}) }= y^{\frac{13}{20}}\\=\sqrt[20]{ y^{13} }\\---------------\)
10. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{1}{4}}}\\= q^{ \frac{5}{6} - \frac{1}{4} }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
11. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{4}{5} - (\frac{-1}{2}) }= x^{\frac{13}{10}}\\=\sqrt[10]{ x^{13} }=|x|.\sqrt[10]{ x^{3} }\\---------------\)
12. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{3} - \frac{2}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)