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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{5}{2} - (\frac{-5}{2}) }= x^{5}\\\\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\dfrac{q^{2}}{q^{\frac{-5}{4}}}\\= q^{ 2 - (\frac{-5}{4}) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{-5}{4}}}\\= y^{ 1 - (\frac{-5}{4}) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{a^{-2}}{a^{\frac{5}{4}}}\\= a^{ -2 - \frac{5}{4} }= a^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ a^{13} }}\\=\frac{1}{|a^{3}|.\sqrt[4]{ a }}=\frac{1}{|a^{3}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{4}|}\\---------------\)
6. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{3}{2}}}\\= x^{ \frac{5}{3} - \frac{3}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{5} - (\frac{-1}{2}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
8. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-4}{5} - \frac{1}{3} }= q^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ q^{17} }}\\=\frac{1}{q.\sqrt[15]{ q^{2} }}=\frac{1}{q.\sqrt[15]{ q^{2} }} \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-5}{3} - (\frac{-5}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
10. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{6} - \frac{3}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{5}{3} - \frac{3}{5} }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)
12. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{4} - \frac{1}{4} }= a^{0}\\=1\\---------------\)