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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{4}{5}}.x^{\frac{1}{2}}\\= x^{ \frac{4}{5} + \frac{1}{2} }= x^{\frac{13}{10}}\\=\sqrt[10]{ x^{13} }=|x|.\sqrt[10]{ x^{3} }\\---------------\)
2. \(a^{1}.a^{\frac{1}{2}}\\= a^{ 1 + \frac{1}{2} }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
3. \(y^{\frac{3}{5}}.y^{2}\\= y^{ \frac{3}{5} + 2 }= y^{\frac{13}{5}}\\=\sqrt[5]{ y^{13} }=y^{2}.\sqrt[5]{ y^{3} }\\---------------\)
4. \(y^{\frac{-2}{3}}.y^{\frac{-3}{5}}\\= y^{ \frac{-2}{3} + (\frac{-3}{5}) }= y^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ y^{19} }}\\=\frac{1}{y.\sqrt[15]{ y^{4} }}=\frac{1}{y.\sqrt[15]{ y^{4} }} \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y^{2}}\\---------------\)
5. \(y^{\frac{-1}{3}}.y^{\frac{-1}{5}}\\= y^{ \frac{-1}{3} + (\frac{-1}{5}) }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
6. \(a^{\frac{-5}{4}}.a^{\frac{4}{5}}\\= a^{ \frac{-5}{4} + \frac{4}{5} }= a^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ a^{9} }}=\frac{1}{\sqrt[20]{ a^{9} }}. \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a|}\\---------------\)
7. \(a^{\frac{4}{3}}.a^{\frac{1}{2}}\\= a^{ \frac{4}{3} + \frac{1}{2} }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
8. \(a^{\frac{-5}{3}}.a^{\frac{-3}{5}}\\= a^{ \frac{-5}{3} + (\frac{-3}{5}) }= a^{\frac{-34}{15}}\\=\frac{1}{\sqrt[15]{ a^{34} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a^{4} }}=\frac{1}{a^{2}.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{3}}\\---------------\)
9. \(x^{1}.x^{\frac{-1}{2}}\\= x^{ 1 + (\frac{-1}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(x^{1}.x^{-1}\\= x^{ 1 + (-1) }= x^{0}\\=1\\---------------\)
11. \(q^{\frac{-5}{3}}.q^{-1}\\= q^{ \frac{-5}{3} + (-1) }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
12. \(a^{\frac{4}{3}}.a^{\frac{-4}{3}}\\= a^{ \frac{4}{3} + (\frac{-4}{3}) }= a^{0}\\=1\\---------------\)