Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{4}{3}}}{y^{-1}}\\= y^{ \frac{4}{3} - (-1) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-3}{5} - (\frac{-2}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
3. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{4} - (\frac{-1}{2}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
4. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-5}{3} - (\frac{-4}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{4}}}\\= a^{ \frac{1}{2} - \frac{5}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
6. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-5}{2} - \frac{5}{3} }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
7. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{5} - \frac{1}{2} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{5} - \frac{5}{4} }= y^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ y^{29} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{9} }}=\frac{1}{|y|.\sqrt[20]{ y^{9} }} \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{1}}\\= x^{ \frac{-5}{4} - 1 }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)
10. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{2}{5} - (\frac{-1}{4}) }= x^{\frac{13}{20}}\\=\sqrt[20]{ x^{13} }\\---------------\)
11. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-2}{3}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{2} - (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)