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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-3}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{-3}{2} . \frac{3}{5} }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
2. \(\left(x^{\frac{2}{5}}\right)^{\frac{-3}{5}}\\= x^{ \frac{2}{5} . (\frac{-3}{5}) }= x^{\frac{-6}{25}}\\=\frac{1}{\sqrt[25]{ x^{6} }}=\frac{1}{\sqrt[25]{ x^{6} }}. \color{purple}{\frac{\sqrt[25]{ x^{19} }}{\sqrt[25]{ x^{19} }}} \\=\frac{\sqrt[25]{ x^{19} }}{x}\\---------------\)
3. \(\left(a^{\frac{4}{5}}\right)^{1}\\= a^{ \frac{4}{5} . 1 }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
4. \(\left(q^{\frac{-3}{4}}\right)^{-1}\\= q^{ \frac{-3}{4} . (-1) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
5. \(\left(a^{\frac{-3}{4}}\right)^{\frac{4}{3}}\\= a^{ \frac{-3}{4} . \frac{4}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
6. \(\left(a^{\frac{2}{3}}\right)^{\frac{2}{5}}\\= a^{ \frac{2}{3} . \frac{2}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
7. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{2} . (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
8. \(\left(q^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{-1}{3} . \frac{2}{3} }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
9. \(\left(x^{-1}\right)^{\frac{2}{3}}\\= x^{ -1 . \frac{2}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
10. \(\left(a^{\frac{-3}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{-3}{5} . \frac{1}{3} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
11. \(\left(q^{\frac{2}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{2}{5} . (\frac{-3}{2}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
12. \(\left(a^{\frac{-1}{5}}\right)^{2}\\= a^{ \frac{-1}{5} . 2 }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)