Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{3}{5} - (\frac{-4}{3}) }= x^{\frac{29}{15}}\\=\sqrt[15]{ x^{29} }=x.\sqrt[15]{ x^{14} }\\---------------\)
2. \(\dfrac{y^{\frac{2}{5}}}{y^{-1}}\\= y^{ \frac{2}{5} - (-1) }= y^{\frac{7}{5}}\\=\sqrt[5]{ y^{7} }=y.\sqrt[5]{ y^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{5} - (\frac{-1}{3}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-3}{4} - (\frac{-3}{4}) }= q^{0}\\=1\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{3} - \frac{2}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
6. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{5}{3} - (\frac{-2}{5}) }= q^{\frac{31}{15}}\\=\sqrt[15]{ q^{31} }=q^{2}.\sqrt[15]{ q }\\---------------\)
7. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-2}{3} - \frac{4}{5} }= y^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ y^{22} }}\\=\frac{1}{y.\sqrt[15]{ y^{7} }}=\frac{1}{y.\sqrt[15]{ y^{7} }} \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y^{2}}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-2}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{1}{6} - (\frac{-3}{4}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
10. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{3}{4} - (\frac{-5}{2}) }= y^{\frac{13}{4}}\\=\sqrt[4]{ y^{13} }=|y^{3}|.\sqrt[4]{ y }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-3}{2} - (\frac{-2}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
12. \(\dfrac{q^{\frac{-5}{6}}}{q^{-1}}\\= q^{ \frac{-5}{6} - (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)