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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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