Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{1}{2} - (\frac{-5}{3}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-3}{5} - \frac{1}{2} }= a^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[10]{ a }}=\frac{1}{|a|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{5}{2}}}\\= q^{ -1 - \frac{5}{2} }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{5}{6}}}\\= y^{ 1 - \frac{5}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
5. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{3}{5}}}\\= x^{ \frac{4}{5} - \frac{3}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
6. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{2}{3} - (\frac{-3}{2}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-3}{4} - (\frac{-2}{3}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-1}{5} - (\frac{-1}{5}) }= q^{0}\\=1\\---------------\)
9. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{5}{3} - (\frac{-1}{5}) }= q^{\frac{28}{15}}\\=\sqrt[15]{ q^{28} }=q.\sqrt[15]{ q^{13} }\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{-3}{4}}}\\= a^{ -1 - (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
11. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{5}{2} - (\frac{-3}{2}) }= q^{4}\\\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{2} - \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)