Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-4}{5} - (\frac{-5}{6}) }= y^{\frac{1}{30}}\\=\sqrt[30]{ y }\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{2}{3} - \frac{1}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-4}{3} - (\frac{-3}{5}) }= y^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ y^{11} }}=\frac{1}{\sqrt[15]{ y^{11} }}. \color{purple}{\frac{\sqrt[15]{ y^{4} }}{\sqrt[15]{ y^{4} }}} \\=\frac{\sqrt[15]{ y^{4} }}{y}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-5}{3} - (\frac{-1}{5}) }= y^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ y^{22} }}\\=\frac{1}{y.\sqrt[15]{ y^{7} }}=\frac{1}{y.\sqrt[15]{ y^{7} }} \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{5}{3}}}{x^{-1}}\\= x^{ \frac{5}{3} - (-1) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{4}{3}}}{q^{1}}\\= q^{ \frac{4}{3} - 1 }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
7. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{2}{3} - (\frac{-2}{5}) }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
8. \(\dfrac{a^{-2}}{a^{\frac{1}{5}}}\\= a^{ -2 - \frac{1}{5} }= a^{\frac{-11}{5}}\\=\frac{1}{\sqrt[5]{ a^{11} }}\\=\frac{1}{a^{2}.\sqrt[5]{ a }}=\frac{1}{a^{2}.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{3}}\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-3}{4} - (\frac{-5}{6}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
11. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
12. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{6} - \frac{2}{3} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)