Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-3}{2} - (\frac{-5}{6}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{5}{2}}}\\= q^{ 1 - \frac{5}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{5}{3}}}\\= a^{ \frac{5}{6} - \frac{5}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{-3}{5}}}\\= q^{ 1 - (\frac{-3}{5}) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
5. \(\dfrac{a^{-2}}{a^{\frac{1}{3}}}\\= a^{ -2 - \frac{1}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-5}{2} - (\frac{-4}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{-5}{4}}}\\= q^{ -1 - (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
8. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-2}{3}) }= q^{0}\\=1\\---------------\)
9. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{4} - \frac{1}{3} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
10. \(\dfrac{q^{\frac{3}{2}}}{q^{1}}\\= q^{ \frac{3}{2} - 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{3} - \frac{2}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)
12. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{3}{2} - (\frac{-2}{5}) }= y^{\frac{19}{10}}\\=\sqrt[10]{ y^{19} }=|y|.\sqrt[10]{ y^{9} }\\---------------\)