Product zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{-1}{2}}.q^{\frac{-1}{3}}\\= q^{ \frac{-1}{2} + (\frac{-1}{3}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
2. \(y^{\frac{-4}{3}}.y^{\frac{-5}{4}}\\= y^{ \frac{-4}{3} + (\frac{-5}{4}) }= y^{\frac{-31}{12}}\\=\frac{1}{\sqrt[12]{ y^{31} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{3}|}\\---------------\)
3. \(a^{\frac{1}{2}}.a^{\frac{-3}{5}}\\= a^{ \frac{1}{2} + (\frac{-3}{5}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
4. \(q^{\frac{-2}{3}}.q^{\frac{1}{2}}\\= q^{ \frac{-2}{3} + \frac{1}{2} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
5. \(y^{\frac{-1}{5}}.y^{\frac{-4}{3}}\\= y^{ \frac{-1}{5} + (\frac{-4}{3}) }= y^{\frac{-23}{15}}\\=\frac{1}{\sqrt[15]{ y^{23} }}\\=\frac{1}{y.\sqrt[15]{ y^{8} }}=\frac{1}{y.\sqrt[15]{ y^{8} }} \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y^{2}}\\---------------\)
6. \(y^{\frac{-1}{5}}.y^{\frac{4}{5}}\\= y^{ \frac{-1}{5} + \frac{4}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
7. \(y^{\frac{5}{2}}.y^{\frac{1}{3}}\\= y^{ \frac{5}{2} + \frac{1}{3} }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
8. \(a^{\frac{5}{6}}.a^{\frac{2}{5}}\\= a^{ \frac{5}{6} + \frac{2}{5} }= a^{\frac{37}{30}}\\=\sqrt[30]{ a^{37} }=|a|.\sqrt[30]{ a^{7} }\\---------------\)
9. \(y^{\frac{2}{3}}.y^{\frac{-1}{4}}\\= y^{ \frac{2}{3} + (\frac{-1}{4}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
10. \(y^{-1}.y^{\frac{-1}{5}}\\= y^{ -1 + (\frac{-1}{5}) }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
11. \(x^{\frac{-1}{3}}.x^{\frac{-2}{3}}\\= x^{ \frac{-1}{3} + (\frac{-2}{3}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(a^{1}.a^{\frac{3}{4}}\\= a^{ 1 + \frac{3}{4} }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)