Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{4}{3} - \frac{5}{4} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
2. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{5}{2} - \frac{4}{3} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{2}}}\\= q^{ \frac{5}{6} - \frac{5}{2} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{4}{5}}}\\= y^{ \frac{4}{5} - \frac{4}{5} }= y^{0}\\=1\\---------------\)
5. \(\dfrac{q^{\frac{-5}{6}}}{q^{-1}}\\= q^{ \frac{-5}{6} - (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{y^{-1}}{y^{2}}\\= y^{ -1 - 2 }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{2} - \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{q^{\frac{-5}{4}}}{q^{-1}}\\= q^{ \frac{-5}{4} - (-1) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{6}}}\\= a^{ \frac{-1}{2} - \frac{1}{6} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
10. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{3}{2} - \frac{1}{2} }= x^{1}\\\\---------------\)
11. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-1}{5} - (\frac{-2}{3}) }= x^{\frac{7}{15}}\\=\sqrt[15]{ x^{7} }\\---------------\)
12. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{5}{6} - (\frac{-1}{2}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)