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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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