Product zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{2}{3}}.q^{\frac{-3}{2}}\\= q^{ \frac{2}{3} + (\frac{-3}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
2. \(y^{\frac{-4}{5}}.y^{\frac{-4}{5}}\\= y^{ \frac{-4}{5} + (\frac{-4}{5}) }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
3. \(x^{\frac{-1}{5}}.x^{\frac{1}{2}}\\= x^{ \frac{-1}{5} + \frac{1}{2} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
4. \(y^{\frac{-1}{3}}.y^{\frac{-4}{3}}\\= y^{ \frac{-1}{3} + (\frac{-4}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
5. \(q^{-1}.q^{-1}\\= q^{ -1 + (-1) }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(x^{\frac{-2}{3}}.x^{1}\\= x^{ \frac{-2}{3} + 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(q^{\frac{-1}{6}}.q^{\frac{-1}{5}}\\= q^{ \frac{-1}{6} + (\frac{-1}{5}) }= q^{\frac{-11}{30}}\\=\frac{1}{\sqrt[30]{ q^{11} }}=\frac{1}{\sqrt[30]{ q^{11} }}. \color{purple}{\frac{\sqrt[30]{ q^{19} }}{\sqrt[30]{ q^{19} }}} \\=\frac{\sqrt[30]{ q^{19} }}{|q|}\\---------------\)
8. \(x^{\frac{5}{6}}.x^{\frac{2}{3}}\\= x^{ \frac{5}{6} + \frac{2}{3} }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
9. \(x^{\frac{-1}{5}}.x^{\frac{4}{3}}\\= x^{ \frac{-1}{5} + \frac{4}{3} }= x^{\frac{17}{15}}\\=\sqrt[15]{ x^{17} }=x.\sqrt[15]{ x^{2} }\\---------------\)
10. \(a^{1}.a^{\frac{-1}{4}}\\= a^{ 1 + (\frac{-1}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
11. \(a^{\frac{3}{4}}.a^{\frac{3}{2}}\\= a^{ \frac{3}{4} + \frac{3}{2} }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
12. \(x^{\frac{1}{3}}.x^{\frac{4}{3}}\\= x^{ \frac{1}{3} + \frac{4}{3} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)