Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{2} - \frac{2}{3} }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
2. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{-4}{3}}}\\= y^{ 1 - (\frac{-4}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{5}) }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{3}{5}}}\\= a^{ -1 - \frac{3}{5} }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-2}{3} - \frac{3}{4} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{a^{2}}{a^{-1}}\\= a^{ 2 - (-1) }= a^{3}\\\\---------------\)
8. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{5}{4} - \frac{1}{2} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{-1}{5}}}\\= x^{ -1 - (\frac{-1}{5}) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
10. \(\dfrac{q^{2}}{q^{\frac{-1}{3}}}\\= q^{ 2 - (\frac{-1}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{x^{\frac{-5}{2}}}{x^{1}}\\= x^{ \frac{-5}{2} - 1 }= x^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ x^{7} } }\\=\frac{1}{|x^{3}|. \sqrt{ x } }=\frac{1}{|x^{3}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{4}|}\\---------------\)
12. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-3}{5} - (\frac{-1}{4}) }= a^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ a^{7} }}=\frac{1}{\sqrt[20]{ a^{7} }}. \color{purple}{\frac{\sqrt[20]{ a^{13} }}{\sqrt[20]{ a^{13} }}} \\=\frac{\sqrt[20]{ a^{13} }}{|a|}\\---------------\)