Product zelfde grondtal

Hoofdmenu Eentje per keer  🖨

Werk uit m.b.v. de rekenregels

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

---

Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-5}{4}}.x^{\frac{1}{4}}\\= x^{ \frac{-5}{4} + \frac{1}{4} }= x^{-1}\\=\frac{1}{x}\\---------------\)
2. \(x^{\frac{3}{4}}.x^{\frac{-5}{4}}\\= x^{ \frac{3}{4} + (\frac{-5}{4}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
3. \(y^{1}.y^{\frac{-3}{4}}\\= y^{ 1 + (\frac{-3}{4}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
4. \(x^{\frac{-3}{4}}.x^{\frac{1}{5}}\\= x^{ \frac{-3}{4} + \frac{1}{5} }= x^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ x^{11} }}=\frac{1}{\sqrt[20]{ x^{11} }}. \color{purple}{\frac{\sqrt[20]{ x^{9} }}{\sqrt[20]{ x^{9} }}} \\=\frac{\sqrt[20]{ x^{9} }}{|x|}\\---------------\)
5. \(q^{\frac{-5}{2}}.q^{-1}\\= q^{ \frac{-5}{2} + (-1) }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
6. \(x^{\frac{-1}{6}}.x^{\frac{-3}{4}}\\= x^{ \frac{-1}{6} + (\frac{-3}{4}) }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
7. \(q^{\frac{-1}{4}}.q^{\frac{-5}{3}}\\= q^{ \frac{-1}{4} + (\frac{-5}{3}) }= q^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{11} }}=\frac{1}{|q|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{2}|}\\---------------\)
8. \(a^{-2}.a^{\frac{1}{5}}\\= a^{ -2 + \frac{1}{5} }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
9. \(y^{\frac{-1}{3}}.y^{\frac{-3}{5}}\\= y^{ \frac{-1}{3} + (\frac{-3}{5}) }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
10. \(q^{\frac{-3}{4}}.q^{\frac{1}{3}}\\= q^{ \frac{-3}{4} + \frac{1}{3} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
11. \(a^{2}.a^{\frac{-2}{5}}\\= a^{ 2 + (\frac{-2}{5}) }= a^{\frac{8}{5}}\\=\sqrt[5]{ a^{8} }=a.\sqrt[5]{ a^{3} }\\---------------\)
12. \(x^{\frac{1}{3}}.x^{\frac{1}{2}}\\= x^{ \frac{1}{3} + \frac{1}{2} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)