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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{2}{3}}\right)^{1}\\= y^{ \frac{2}{3} . 1 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
2. \(\left(a^{\frac{-1}{3}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-1}{3} . (\frac{-1}{5}) }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
3. \(\left(x^{\frac{2}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{2}{3} . (\frac{-5}{6}) }= x^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ x^{5} }}=\frac{1}{\sqrt[9]{ x^{5} }}. \color{purple}{\frac{\sqrt[9]{ x^{4} }}{\sqrt[9]{ x^{4} }}} \\=\frac{\sqrt[9]{ x^{4} }}{x}\\---------------\)
4. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-3}{5} . (\frac{-3}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
5. \(\left(x^{\frac{-1}{6}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-1}{6} . (\frac{-2}{3}) }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
6. \(\left(x^{\frac{3}{5}}\right)^{\frac{5}{3}}\\= x^{ \frac{3}{5} . \frac{5}{3} }= x^{1}\\\\---------------\)
7. \(\left(a^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{4} . \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
8. \(\left(a^{\frac{4}{5}}\right)^{\frac{-5}{3}}\\= a^{ \frac{4}{5} . (\frac{-5}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
9. \(\left(q^{\frac{-1}{5}}\right)^{\frac{1}{3}}\\= q^{ \frac{-1}{5} . \frac{1}{3} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{2} . (\frac{-3}{4}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
11. \(\left(y^{\frac{5}{6}}\right)^{\frac{1}{3}}\\= y^{ \frac{5}{6} . \frac{1}{3} }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
12. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)