Quotiënt zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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