Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{4} - (\frac{-1}{3}) }= y^{\frac{19}{12}}\\=\sqrt[12]{ y^{19} }=|y|.\sqrt[12]{ y^{7} }\\---------------\)
2. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{5} - \frac{3}{2} }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
4. \(\dfrac{y^{\frac{-3}{2}}}{y^{-1}}\\= y^{ \frac{-3}{2} - (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{-1}{6}}}\\= q^{ -1 - (\frac{-1}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{2}{3} - \frac{2}{3} }= x^{0}\\=1\\---------------\)
7. \(\dfrac{q^{\frac{3}{4}}}{q^{1}}\\= q^{ \frac{3}{4} - 1 }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
8. \(\dfrac{a^{\frac{5}{6}}}{a^{1}}\\= a^{ \frac{5}{6} - 1 }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{2} - (\frac{-2}{3}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{5}{2}}}\\= q^{ -1 - \frac{5}{2} }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
11. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{6} - \frac{1}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
12. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)