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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(q^{\frac{-2}{3}}.q^{2}\\= q^{ \frac{-2}{3} + 2 }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
2. \(y^{\frac{3}{5}}.y^{\frac{-2}{5}}\\= y^{ \frac{3}{5} + (\frac{-2}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
3. \(q^{\frac{-1}{2}}.q^{\frac{-1}{4}}\\= q^{ \frac{-1}{2} + (\frac{-1}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
4. \(y^{\frac{-5}{3}}.y^{\frac{-5}{3}}\\= y^{ \frac{-5}{3} + (\frac{-5}{3}) }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
5. \(y^{\frac{-4}{5}}.y^{\frac{-4}{3}}\\= y^{ \frac{-4}{5} + (\frac{-4}{3}) }= y^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ y^{32} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{3}}\\---------------\)
6. \(a^{\frac{-2}{5}}.a^{\frac{-4}{5}}\\= a^{ \frac{-2}{5} + (\frac{-4}{5}) }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
7. \(a^{\frac{-1}{3}}.a^{\frac{5}{6}}\\= a^{ \frac{-1}{3} + \frac{5}{6} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
8. \(y^{-2}.y^{\frac{-5}{3}}\\= y^{ -2 + (\frac{-5}{3}) }= y^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ y^{11} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{3}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{4}}\\---------------\)
9. \(a^{1}.a^{\frac{-3}{5}}\\= a^{ 1 + (\frac{-3}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
10. \(x^{1}.x^{-1}\\= x^{ 1 + (-1) }= x^{0}\\=1\\---------------\)
11. \(q^{\frac{1}{2}}.q^{\frac{-3}{2}}\\= q^{ \frac{1}{2} + (\frac{-3}{2}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
12. \(q^{\frac{1}{2}}.q^{\frac{-1}{4}}\\= q^{ \frac{1}{2} + (\frac{-1}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)