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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-2}{5}}\right)^{\frac{-2}{5}}\\= a^{ \frac{-2}{5} . (\frac{-2}{5}) }= a^{\frac{4}{25}}\\=\sqrt[25]{ a^{4} }\\---------------\)
2. \(\left(y^{1}\right)^{\frac{-1}{4}}\\= y^{ 1 . (\frac{-1}{4}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{1}{5}}\\= a^{ -1 . \frac{1}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\left(y^{\frac{2}{3}}\right)^{-1}\\= y^{ \frac{2}{3} . (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\left(y^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{-1}{2} . \frac{1}{3} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\left(y^{-1}\right)^{\frac{3}{5}}\\= y^{ -1 . \frac{3}{5} }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
7. \(\left(y^{\frac{1}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{1}{3} . \frac{5}{2} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
8. \(\left(q^{\frac{4}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{4}{5} . (\frac{-1}{5}) }= q^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ q^{4} }}=\frac{1}{\sqrt[25]{ q^{4} }}. \color{purple}{\frac{\sqrt[25]{ q^{21} }}{\sqrt[25]{ q^{21} }}} \\=\frac{\sqrt[25]{ q^{21} }}{q}\\---------------\)
9. \(\left(q^{\frac{1}{5}}\right)^{1}\\= q^{ \frac{1}{5} . 1 }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
10. \(\left(a^{\frac{5}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{5}{2} . \frac{2}{3} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
11. \(\left(q^{\frac{2}{3}}\right)^{1}\\= q^{ \frac{2}{3} . 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= y^{ \frac{1}{2} . (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)