Product zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

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