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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(y^{\frac{-5}{6}}.y^{\frac{5}{3}}\\= y^{ \frac{-5}{6} + \frac{5}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
2. \(a^{-1}.a^{-1}\\= a^{ -1 + (-1) }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
3. \(x^{\frac{5}{6}}.x^{\frac{-1}{4}}\\= x^{ \frac{5}{6} + (\frac{-1}{4}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
4. \(y^{1}.y^{-1}\\= y^{ 1 + (-1) }= y^{0}\\=1\\---------------\)
5. \(a^{\frac{2}{5}}.a^{\frac{-1}{5}}\\= a^{ \frac{2}{5} + (\frac{-1}{5}) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
6. \(y^{-2}.y^{-1}\\= y^{ -2 + (-1) }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
7. \(a^{\frac{3}{4}}.a^{\frac{5}{4}}\\= a^{ \frac{3}{4} + \frac{5}{4} }= a^{2}\\\\---------------\)
8. \(a^{\frac{-5}{3}}.a^{\frac{-5}{3}}\\= a^{ \frac{-5}{3} + (\frac{-5}{3}) }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
9. \(a^{\frac{5}{4}}.a^{\frac{-1}{4}}\\= a^{ \frac{5}{4} + (\frac{-1}{4}) }= a^{1}\\\\---------------\)
10. \(a^{\frac{-1}{5}}.a^{\frac{-1}{3}}\\= a^{ \frac{-1}{5} + (\frac{-1}{3}) }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
11. \(q^{\frac{-1}{6}}.q^{\frac{2}{5}}\\= q^{ \frac{-1}{6} + \frac{2}{5} }= q^{\frac{7}{30}}\\=\sqrt[30]{ q^{7} }\\---------------\)
12. \(y^{-1}.y^{\frac{-3}{5}}\\= y^{ -1 + (\frac{-3}{5}) }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)