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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-1}{5}}.x^{\frac{3}{2}}\\= x^{ \frac{-1}{5} + \frac{3}{2} }= x^{\frac{13}{10}}\\=\sqrt[10]{ x^{13} }=|x|.\sqrt[10]{ x^{3} }\\---------------\)
2. \(q^{\frac{-5}{2}}.q^{\frac{2}{3}}\\= q^{ \frac{-5}{2} + \frac{2}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
3. \(q^{\frac{-1}{5}}.q^{\frac{5}{2}}\\= q^{ \frac{-1}{5} + \frac{5}{2} }= q^{\frac{23}{10}}\\=\sqrt[10]{ q^{23} }=|q^{2}|.\sqrt[10]{ q^{3} }\\---------------\)
4. \(y^{2}.y^{\frac{3}{5}}\\= y^{ 2 + \frac{3}{5} }= y^{\frac{13}{5}}\\=\sqrt[5]{ y^{13} }=y^{2}.\sqrt[5]{ y^{3} }\\---------------\)
5. \(x^{\frac{-1}{3}}.x^{\frac{-1}{6}}\\= x^{ \frac{-1}{3} + (\frac{-1}{6}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
6. \(a^{\frac{2}{3}}.a^{\frac{-2}{3}}\\= a^{ \frac{2}{3} + (\frac{-2}{3}) }= a^{0}\\=1\\---------------\)
7. \(a^{\frac{1}{2}}.a^{\frac{1}{4}}\\= a^{ \frac{1}{2} + \frac{1}{4} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
8. \(a^{\frac{-1}{5}}.a^{\frac{3}{5}}\\= a^{ \frac{-1}{5} + \frac{3}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
9. \(a^{\frac{-3}{4}}.a^{\frac{1}{2}}\\= a^{ \frac{-3}{4} + \frac{1}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
10. \(x^{\frac{-1}{4}}.x^{\frac{-2}{3}}\\= x^{ \frac{-1}{4} + (\frac{-2}{3}) }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
11. \(q^{\frac{1}{6}}.q^{\frac{1}{4}}\\= q^{ \frac{1}{6} + \frac{1}{4} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
12. \(x^{\frac{-1}{3}}.x^{\frac{3}{5}}\\= x^{ \frac{-1}{3} + \frac{3}{5} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)