Product zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{-1}.y^{\frac{1}{2}}\\= y^{ -1 + \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(x^{\frac{1}{6}}.x^{-1}\\= x^{ \frac{1}{6} + (-1) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
3. \(q^{\frac{5}{2}}.q^{\frac{5}{3}}\\= q^{ \frac{5}{2} + \frac{5}{3} }= q^{\frac{25}{6}}\\=\sqrt[6]{ q^{25} }=|q^{4}|.\sqrt[6]{ q }\\---------------\)
4. \(q^{\frac{1}{4}}.q^{\frac{5}{4}}\\= q^{ \frac{1}{4} + \frac{5}{4} }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
5. \(x^{\frac{-5}{4}}.x^{\frac{-4}{5}}\\= x^{ \frac{-5}{4} + (\frac{-4}{5}) }= x^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ x^{41} }}\\=\frac{1}{|x^{2}|.\sqrt[20]{ x }}=\frac{1}{|x^{2}|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{3}|}\\---------------\)
6. \(y^{\frac{-4}{3}}.y^{\frac{2}{3}}\\= y^{ \frac{-4}{3} + \frac{2}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
7. \(y^{\frac{5}{3}}.y^{\frac{-1}{5}}\\= y^{ \frac{5}{3} + (\frac{-1}{5}) }= y^{\frac{22}{15}}\\=\sqrt[15]{ y^{22} }=y.\sqrt[15]{ y^{7} }\\---------------\)
8. \(y^{\frac{1}{2}}.y^{\frac{5}{3}}\\= y^{ \frac{1}{2} + \frac{5}{3} }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
9. \(y^{\frac{-1}{4}}.y^{\frac{1}{2}}\\= y^{ \frac{-1}{4} + \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
10. \(x^{-1}.x^{\frac{4}{5}}\\= x^{ -1 + \frac{4}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
11. \(q^{-1}.q^{1}\\= q^{ -1 + 1 }= q^{0}\\=1\\---------------\)
12. \(y^{\frac{1}{2}}.y^{\frac{5}{6}}\\= y^{ \frac{1}{2} + \frac{5}{6} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)