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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{5}}\right)^{\frac{1}{5}}\\= y^{ \frac{-3}{5} . \frac{1}{5} }= y^{\frac{-3}{25}}\\=\frac{1}{\sqrt[25]{ y^{3} }}=\frac{1}{\sqrt[25]{ y^{3} }}. \color{purple}{\frac{\sqrt[25]{ y^{22} }}{\sqrt[25]{ y^{22} }}} \\=\frac{\sqrt[25]{ y^{22} }}{y}\\---------------\)
2. \(\left(y^{1}\right)^{\frac{-1}{6}}\\= y^{ 1 . (\frac{-1}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
3. \(\left(a^{\frac{1}{5}}\right)^{-1}\\= a^{ \frac{1}{5} . (-1) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\left(x^{\frac{-2}{3}}\right)^{-2}\\= x^{ \frac{-2}{3} . (-2) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
5. \(\left(a^{\frac{-2}{5}}\right)^{\frac{1}{4}}\\= a^{ \frac{-2}{5} . \frac{1}{4} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
6. \(\left(q^{\frac{-1}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{-1}{3} . (\frac{-1}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
7. \(\left(y^{\frac{1}{2}}\right)^{\frac{3}{2}}\\= y^{ \frac{1}{2} . \frac{3}{2} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
8. \(\left(x^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{2} . (\frac{-1}{2}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
9. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-3}{2}}\\= q^{ \frac{-1}{2} . (\frac{-3}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
10. \(\left(x^{1}\right)^{\frac{5}{4}}\\= x^{ 1 . \frac{5}{4} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
11. \(\left(a^{\frac{-2}{5}}\right)^{\frac{5}{6}}\\= a^{ \frac{-2}{5} . \frac{5}{6} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
12. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)