Product zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{-4}{3}}.q^{\frac{-1}{5}}\\= q^{ \frac{-4}{3} + (\frac{-1}{5}) }= q^{\frac{-23}{15}}\\=\frac{1}{\sqrt[15]{ q^{23} }}\\=\frac{1}{q.\sqrt[15]{ q^{8} }}=\frac{1}{q.\sqrt[15]{ q^{8} }} \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q^{2}}\\---------------\)
2. \(y^{\frac{-2}{3}}.y^{\frac{-5}{2}}\\= y^{ \frac{-2}{3} + (\frac{-5}{2}) }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
3. \(x^{-1}.x^{\frac{-1}{2}}\\= x^{ -1 + (\frac{-1}{2}) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
4. \(x^{\frac{-5}{3}}.x^{\frac{-3}{5}}\\= x^{ \frac{-5}{3} + (\frac{-3}{5}) }= x^{\frac{-34}{15}}\\=\frac{1}{\sqrt[15]{ x^{34} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x^{4} }}=\frac{1}{x^{2}.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{3}}\\---------------\)
5. \(a^{\frac{5}{2}}.a^{1}\\= a^{ \frac{5}{2} + 1 }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
6. \(y^{-1}.y^{\frac{4}{5}}\\= y^{ -1 + \frac{4}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
7. \(x^{1}.x^{\frac{-1}{3}}\\= x^{ 1 + (\frac{-1}{3}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
8. \(a^{\frac{4}{5}}.a^{-1}\\= a^{ \frac{4}{5} + (-1) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
9. \(y^{1}.y^{\frac{-5}{6}}\\= y^{ 1 + (\frac{-5}{6}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
10. \(x^{\frac{-3}{5}}.x^{\frac{-4}{3}}\\= x^{ \frac{-3}{5} + (\frac{-4}{3}) }= x^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ x^{29} }}\\=\frac{1}{x.\sqrt[15]{ x^{14} }}=\frac{1}{x.\sqrt[15]{ x^{14} }} \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x^{2}}\\---------------\)
11. \(q^{\frac{-2}{5}}.q^{\frac{-1}{5}}\\= q^{ \frac{-2}{5} + (\frac{-1}{5}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
12. \(y^{\frac{-1}{2}}.y^{\frac{-5}{6}}\\= y^{ \frac{-1}{2} + (\frac{-5}{6}) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)