Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{4}{3}}}{x^{2}}\\= x^{ \frac{4}{3} - 2 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
2. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{2} - \frac{1}{2} }= q^{2}\\\\---------------\)
3. \(\dfrac{q^{2}}{q^{\frac{1}{4}}}\\= q^{ 2 - \frac{1}{4} }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
4. \(\dfrac{q^{2}}{q^{\frac{-1}{2}}}\\= q^{ 2 - (\frac{-1}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{-5}{4}}}\\= a^{ -1 - (\frac{-5}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-5}{6} - \frac{1}{4} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
8. \(\dfrac{a^{\frac{-1}{5}}}{a^{-1}}\\= a^{ \frac{-1}{5} - (-1) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{-3}{5}}}\\= a^{ -1 - (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
10. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\\= y^{ \frac{1}{3} - (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
11. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-4}{3} - \frac{2}{5} }= y^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ y^{26} }}\\=\frac{1}{y.\sqrt[15]{ y^{11} }}=\frac{1}{y.\sqrt[15]{ y^{11} }} \color{purple}{\frac{\sqrt[15]{ y^{4} }}{\sqrt[15]{ y^{4} }}} \\=\frac{\sqrt[15]{ y^{4} }}{y^{2}}\\---------------\)
12. \(\dfrac{x^{1}}{x^{-1}}\\= x^{ 1 - (-1) }= x^{2}\\\\---------------\)