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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{5}}\right)^{\frac{2}{5}}\\= q^{ \frac{2}{5} . \frac{2}{5} }= q^{\frac{4}{25}}\\=\sqrt[25]{ q^{4} }\\---------------\)
2. \(\left(a^{-2}\right)^{\frac{-1}{5}}\\= a^{ -2 . (\frac{-1}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
3. \(\left(x^{\frac{-1}{6}}\right)^{1}\\= x^{ \frac{-1}{6} . 1 }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
4. \(\left(y^{\frac{-5}{3}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-5}{3} . (\frac{-5}{3}) }= y^{\frac{25}{9}}\\=\sqrt[9]{ y^{25} }=y^{2}.\sqrt[9]{ y^{7} }\\---------------\)
5. \(\left(q^{1}\right)^{\frac{1}{3}}\\= q^{ 1 . \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\left(a^{1}\right)^{\frac{-5}{4}}\\= a^{ 1 . (\frac{-5}{4}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
7. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-4}{5} . (\frac{-3}{2}) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
8. \(\left(y^{\frac{2}{5}}\right)^{\frac{-1}{3}}\\= y^{ \frac{2}{5} . (\frac{-1}{3}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
9. \(\left(q^{\frac{-2}{5}}\right)^{2}\\= q^{ \frac{-2}{5} . 2 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
10. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-5}{3} . (\frac{-4}{5}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
11. \(\left(x^{\frac{-1}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{3} . (\frac{-5}{6}) }= x^{\frac{5}{18}}\\=\sqrt[18]{ x^{5} }\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-1}{2} . (\frac{-1}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)