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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-4}{5}}.x^{\frac{2}{3}}\\= x^{ \frac{-4}{5} + \frac{2}{3} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
2. \(x^{\frac{1}{2}}.x^{1}\\= x^{ \frac{1}{2} + 1 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(y^{\frac{-5}{4}}.y^{\frac{-1}{6}}\\= y^{ \frac{-5}{4} + (\frac{-1}{6}) }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
4. \(x^{\frac{-5}{3}}.x^{\frac{-1}{2}}\\= x^{ \frac{-5}{3} + (\frac{-1}{2}) }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
5. \(q^{-1}.q^{\frac{-2}{3}}\\= q^{ -1 + (\frac{-2}{3}) }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
6. \(y^{-1}.y^{\frac{1}{5}}\\= y^{ -1 + \frac{1}{5} }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
7. \(q^{\frac{-4}{3}}.q^{1}\\= q^{ \frac{-4}{3} + 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
8. \(a^{1}.a^{\frac{-3}{2}}\\= a^{ 1 + (\frac{-3}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(q^{\frac{-2}{3}}.q^{\frac{-3}{5}}\\= q^{ \frac{-2}{3} + (\frac{-3}{5}) }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
10. \(a^{\frac{3}{4}}.a^{\frac{-1}{2}}\\= a^{ \frac{3}{4} + (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
11. \(x^{\frac{-2}{3}}.x^{\frac{-5}{3}}\\= x^{ \frac{-2}{3} + (\frac{-5}{3}) }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
12. \(y^{1}.y^{\frac{-5}{6}}\\= y^{ 1 + (\frac{-5}{6}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)