Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{1}{2} - \frac{4}{5} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{-3}{2}}}\\= a^{ 1 - (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{3}{5} - (\frac{-5}{4}) }= y^{\frac{37}{20}}\\=\sqrt[20]{ y^{37} }=|y|.\sqrt[20]{ y^{17} }\\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{1}{4}}}\\= q^{ -1 - \frac{1}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{-3}{5}}}{q^{-1}}\\= q^{ \frac{-3}{5} - (-1) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-1}{4}}}\\= a^{ -1 - (\frac{-1}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-1}{3} - (\frac{-3}{4}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
9. \(\dfrac{x^{\frac{-5}{3}}}{x^{1}}\\= x^{ \frac{-5}{3} - 1 }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
10. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{4}{3} - \frac{3}{4} }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{3} - (\frac{-2}{5}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
12. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-2}{5} - (\frac{-1}{4}) }= y^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ y^{3} }}=\frac{1}{\sqrt[20]{ y^{3} }}. \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y|}\\---------------\)