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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{1}{4}}.y^{1}\\= y^{ \frac{1}{4} + 1 }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
2. \(q^{-1}.q^{\frac{-2}{5}}\\= q^{ -1 + (\frac{-2}{5}) }= q^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ q^{7} }}\\=\frac{1}{q.\sqrt[5]{ q^{2} }}=\frac{1}{q.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{2}}\\---------------\)
3. \(x^{\frac{3}{5}}.x^{2}\\= x^{ \frac{3}{5} + 2 }= x^{\frac{13}{5}}\\=\sqrt[5]{ x^{13} }=x^{2}.\sqrt[5]{ x^{3} }\\---------------\)
4. \(q^{2}.q^{\frac{-4}{5}}\\= q^{ 2 + (\frac{-4}{5}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
5. \(q^{\frac{3}{2}}.q^{\frac{1}{5}}\\= q^{ \frac{3}{2} + \frac{1}{5} }= q^{\frac{17}{10}}\\=\sqrt[10]{ q^{17} }=|q|.\sqrt[10]{ q^{7} }\\---------------\)
6. \(x^{1}.x^{\frac{2}{3}}\\= x^{ 1 + \frac{2}{3} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
7. \(y^{\frac{-1}{3}}.y^{\frac{-1}{4}}\\= y^{ \frac{-1}{3} + (\frac{-1}{4}) }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
8. \(y^{\frac{-1}{2}}.y^{\frac{4}{3}}\\= y^{ \frac{-1}{2} + \frac{4}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
9. \(q^{1}.q^{1}\\= q^{ 1 + 1 }= q^{2}\\\\---------------\)
10. \(q^{\frac{5}{4}}.q^{-1}\\= q^{ \frac{5}{4} + (-1) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
11. \(x^{\frac{-4}{3}}.x^{1}\\= x^{ \frac{-4}{3} + 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
12. \(x^{\frac{4}{5}}.x^{\frac{4}{3}}\\= x^{ \frac{4}{5} + \frac{4}{3} }= x^{\frac{32}{15}}\\=\sqrt[15]{ x^{32} }=x^{2}.\sqrt[15]{ x^{2} }\\---------------\)