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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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