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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{-1}{3}}.x^{\frac{3}{4}}\\= x^{ \frac{-1}{3} + \frac{3}{4} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
2. \(y^{\frac{1}{2}}.y^{\frac{3}{2}}\\= y^{ \frac{1}{2} + \frac{3}{2} }= y^{2}\\\\---------------\)
3. \(x^{\frac{1}{2}}.x^{\frac{3}{4}}\\= x^{ \frac{1}{2} + \frac{3}{4} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
4. \(y^{-1}.y^{\frac{-5}{3}}\\= y^{ -1 + (\frac{-5}{3}) }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
5. \(x^{-1}.x^{\frac{2}{3}}\\= x^{ -1 + \frac{2}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(a^{\frac{-5}{4}}.a^{-1}\\= a^{ \frac{-5}{4} + (-1) }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
7. \(q^{\frac{5}{2}}.q^{\frac{-1}{3}}\\= q^{ \frac{5}{2} + (\frac{-1}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
8. \(x^{\frac{3}{5}}.x^{\frac{1}{4}}\\= x^{ \frac{3}{5} + \frac{1}{4} }= x^{\frac{17}{20}}\\=\sqrt[20]{ x^{17} }\\---------------\)
9. \(a^{\frac{1}{2}}.a^{\frac{5}{4}}\\= a^{ \frac{1}{2} + \frac{5}{4} }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
10. \(x^{\frac{5}{4}}.x^{-1}\\= x^{ \frac{5}{4} + (-1) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
11. \(y^{\frac{-1}{3}}.y^{\frac{1}{3}}\\= y^{ \frac{-1}{3} + \frac{1}{3} }= y^{0}\\=1\\---------------\)
12. \(a^{1}.a^{\frac{-2}{3}}\\= a^{ 1 + (\frac{-2}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)