Product zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{-1}{4}}.y^{-1}\\= y^{ \frac{-1}{4} + (-1) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
2. \(y^{\frac{-1}{6}}.y^{\frac{-1}{4}}\\= y^{ \frac{-1}{6} + (\frac{-1}{4}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
3. \(y^{\frac{-5}{3}}.y^{\frac{-5}{4}}\\= y^{ \frac{-5}{3} + (\frac{-5}{4}) }= y^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ y^{35} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{11} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{11} }} \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y^{3}|}\\---------------\)
4. \(x^{\frac{5}{6}}.x^{-1}\\= x^{ \frac{5}{6} + (-1) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
5. \(q^{\frac{-2}{3}}.q^{\frac{5}{6}}\\= q^{ \frac{-2}{3} + \frac{5}{6} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(q^{-2}.q^{\frac{-1}{3}}\\= q^{ -2 + (\frac{-1}{3}) }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
7. \(x^{\frac{-1}{6}}.x^{\frac{5}{3}}\\= x^{ \frac{-1}{6} + \frac{5}{3} }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
8. \(a^{1}.a^{\frac{-5}{2}}\\= a^{ 1 + (\frac{-5}{2}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
9. \(q^{\frac{-1}{6}}.q^{\frac{-1}{2}}\\= q^{ \frac{-1}{6} + (\frac{-1}{2}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
10. \(q^{\frac{3}{5}}.q^{1}\\= q^{ \frac{3}{5} + 1 }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
11. \(x^{\frac{-2}{5}}.x^{\frac{3}{4}}\\= x^{ \frac{-2}{5} + \frac{3}{4} }= x^{\frac{7}{20}}\\=\sqrt[20]{ x^{7} }\\---------------\)
12. \(q^{-1}.q^{\frac{1}{5}}\\= q^{ -1 + \frac{1}{5} }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)