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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{1}\right)^{\frac{-1}{5}}\\= q^{ 1 . (\frac{-1}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
2. \(\left(a^{\frac{-5}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{-5}{2} . \frac{5}{2} }= a^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ a^{25} }}\\=\frac{1}{|a^{6}|.\sqrt[4]{ a }}=\frac{1}{|a^{6}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{7}|}\\---------------\)
3. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{-2}{3}}\\= a^{ -1 . (\frac{-2}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\left(a^{\frac{2}{3}}\right)^{\frac{-2}{5}}\\= a^{ \frac{2}{3} . (\frac{-2}{5}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
6. \(\left(y^{\frac{1}{4}}\right)^{1}\\= y^{ \frac{1}{4} . 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
7. \(\left(x^{\frac{-3}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-3}{5} . \frac{2}{3} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
8. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{3} . (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
9. \(\left(y^{\frac{2}{3}}\right)^{1}\\= y^{ \frac{2}{3} . 1 }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
10. \(\left(a^{\frac{5}{6}}\right)^{\frac{1}{6}}\\= a^{ \frac{5}{6} . \frac{1}{6} }= a^{\frac{5}{36}}\\=\sqrt[36]{ a^{5} }\\---------------\)
11. \(\left(x^{\frac{-5}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{-5}{2} . \frac{4}{3} }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)
12. \(\left(a^{\frac{-5}{6}}\right)^{\frac{2}{5}}\\= a^{ \frac{-5}{6} . \frac{2}{5} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)