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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(x^{\frac{4}{5}}.x^{\frac{-5}{4}}\\= x^{ \frac{4}{5} + (\frac{-5}{4}) }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
2. \(q^{\frac{-4}{5}}.q^{-1}\\= q^{ \frac{-4}{5} + (-1) }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
3. \(a^{\frac{3}{2}}.a^{\frac{-3}{2}}\\= a^{ \frac{3}{2} + (\frac{-3}{2}) }= a^{0}\\=1\\---------------\)
4. \(y^{\frac{5}{2}}.y^{\frac{3}{4}}\\= y^{ \frac{5}{2} + \frac{3}{4} }= y^{\frac{13}{4}}\\=\sqrt[4]{ y^{13} }=|y^{3}|.\sqrt[4]{ y }\\---------------\)
5. \(q^{\frac{1}{5}}.q^{\frac{-1}{2}}\\= q^{ \frac{1}{5} + (\frac{-1}{2}) }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
6. \(q^{\frac{1}{3}}.q^{\frac{4}{3}}\\= q^{ \frac{1}{3} + \frac{4}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
7. \(y^{\frac{2}{3}}.y^{\frac{5}{2}}\\= y^{ \frac{2}{3} + \frac{5}{2} }= y^{\frac{19}{6}}\\=\sqrt[6]{ y^{19} }=|y^{3}|.\sqrt[6]{ y }\\---------------\)
8. \(q^{1}.q^{\frac{-5}{4}}\\= q^{ 1 + (\frac{-5}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
9. \(a^{\frac{2}{3}}.a^{\frac{-2}{5}}\\= a^{ \frac{2}{3} + (\frac{-2}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
10. \(y^{\frac{1}{2}}.y^{\frac{1}{3}}\\= y^{ \frac{1}{2} + \frac{1}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
11. \(a^{\frac{-1}{2}}.a^{\frac{3}{2}}\\= a^{ \frac{-1}{2} + \frac{3}{2} }= a^{1}\\\\---------------\)
12. \(q^{1}.q^{\frac{-1}{2}}\\= q^{ 1 + (\frac{-1}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)