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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{4}}\right)^{\frac{4}{3}}\\= x^{ \frac{-1}{4} . \frac{4}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
2. \(\left(a^{\frac{4}{5}}\right)^{\frac{-3}{5}}\\= a^{ \frac{4}{5} . (\frac{-3}{5}) }= a^{\frac{-12}{25}}\\=\frac{1}{\sqrt[25]{ a^{12} }}=\frac{1}{\sqrt[25]{ a^{12} }}. \color{purple}{\frac{\sqrt[25]{ a^{13} }}{\sqrt[25]{ a^{13} }}} \\=\frac{\sqrt[25]{ a^{13} }}{a}\\---------------\)
3. \(\left(y^{2}\right)^{\frac{-4}{3}}\\= y^{ 2 . (\frac{-4}{3}) }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
4. \(\left(x^{\frac{-3}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-3}{2} . \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
5. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-3}{5}}\\= a^{ \frac{-1}{2} . (\frac{-3}{5}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
6. \(\left(x^{\frac{1}{6}}\right)^{\frac{-1}{5}}\\= x^{ \frac{1}{6} . (\frac{-1}{5}) }= x^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ x }}=\frac{1}{\sqrt[30]{ x }}. \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x|}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-4}{5}}\\= a^{ -1 . (\frac{-4}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
8. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\left(q^{\frac{-1}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{-1}{5} . \frac{2}{3} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= x^{ \frac{-1}{2} . \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
11. \(\left(x^{\frac{-1}{6}}\right)^{-1}\\= x^{ \frac{-1}{6} . (-1) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
12. \(\left(a^{\frac{1}{4}}\right)^{1}\\= a^{ \frac{1}{4} . 1 }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)