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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{1}.y^{\frac{1}{2}}\\= y^{ 1 + \frac{1}{2} }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(y^{\frac{-5}{3}}.y^{\frac{-3}{4}}\\= y^{ \frac{-5}{3} + (\frac{-3}{4}) }= y^{\frac{-29}{12}}\\=\frac{1}{\sqrt[12]{ y^{29} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{3}|}\\---------------\)
3. \(x^{\frac{1}{5}}.x^{\frac{1}{2}}\\= x^{ \frac{1}{5} + \frac{1}{2} }= x^{\frac{7}{10}}\\=\sqrt[10]{ x^{7} }\\---------------\)
4. \(y^{\frac{-5}{2}}.y^{\frac{1}{3}}\\= y^{ \frac{-5}{2} + \frac{1}{3} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
5. \(y^{\frac{-3}{4}}.y^{-1}\\= y^{ \frac{-3}{4} + (-1) }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
6. \(q^{\frac{-1}{3}}.q^{\frac{-1}{3}}\\= q^{ \frac{-1}{3} + (\frac{-1}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
7. \(q^{\frac{2}{5}}.q^{-1}\\= q^{ \frac{2}{5} + (-1) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
8. \(y^{\frac{-1}{4}}.y^{\frac{5}{6}}\\= y^{ \frac{-1}{4} + \frac{5}{6} }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
9. \(x^{\frac{-4}{3}}.x^{\frac{1}{2}}\\= x^{ \frac{-4}{3} + \frac{1}{2} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
10. \(q^{\frac{4}{5}}.q^{\frac{2}{5}}\\= q^{ \frac{4}{5} + \frac{2}{5} }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
11. \(y^{\frac{-1}{2}}.y^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} + (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
12. \(x^{1}.x^{\frac{4}{3}}\\= x^{ 1 + \frac{4}{3} }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)