Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-2}{3}}}{x^{1}}\\= x^{ \frac{-2}{3} - 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{4}{3} - (\frac{-1}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{3}}}{x^{-1}}\\= x^{ \frac{-5}{3} - (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
5. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{4}{5} - (\frac{-2}{3}) }= y^{\frac{22}{15}}\\=\sqrt[15]{ y^{22} }=y.\sqrt[15]{ y^{7} }\\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-2}{3} - \frac{3}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
7. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-5}{6} - (\frac{-5}{4}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
8. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-5}{2} - (\frac{-3}{5}) }= q^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{9} }}=\frac{1}{|q|.\sqrt[10]{ q^{9} }} \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{2}{3} - \frac{1}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{1}{2} - (\frac{-5}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{-5}{2}}}\\= q^{ 1 - (\frac{-5}{2}) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)