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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{-5}{3}}.q^{1}\\= q^{ \frac{-5}{3} + 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
2. \(x^{-1}.x^{\frac{4}{5}}\\= x^{ -1 + \frac{4}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
3. \(y^{\frac{5}{4}}.y^{\frac{2}{5}}\\= y^{ \frac{5}{4} + \frac{2}{5} }= y^{\frac{33}{20}}\\=\sqrt[20]{ y^{33} }=|y|.\sqrt[20]{ y^{13} }\\---------------\)
4. \(x^{-2}.x^{\frac{3}{2}}\\= x^{ -2 + \frac{3}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
5. \(q^{\frac{1}{3}}.q^{\frac{-1}{3}}\\= q^{ \frac{1}{3} + (\frac{-1}{3}) }= q^{0}\\=1\\---------------\)
6. \(a^{\frac{1}{5}}.a^{1}\\= a^{ \frac{1}{5} + 1 }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
7. \(a^{1}.a^{\frac{4}{3}}\\= a^{ 1 + \frac{4}{3} }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
8. \(x^{\frac{-2}{3}}.x^{\frac{-5}{3}}\\= x^{ \frac{-2}{3} + (\frac{-5}{3}) }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
9. \(a^{1}.a^{\frac{-1}{2}}\\= a^{ 1 + (\frac{-1}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(y^{\frac{1}{6}}.y^{\frac{-3}{2}}\\= y^{ \frac{1}{6} + (\frac{-3}{2}) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
11. \(y^{\frac{1}{6}}.y^{\frac{-5}{6}}\\= y^{ \frac{1}{6} + (\frac{-5}{6}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
12. \(q^{\frac{-1}{2}}.q^{\frac{5}{3}}\\= q^{ \frac{-1}{2} + \frac{5}{3} }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)