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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{3}{4}}\right)^{\frac{-5}{2}}\\= x^{ \frac{3}{4} . (\frac{-5}{2}) }= x^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ x^{15} }}\\=\frac{1}{|x|.\sqrt[8]{ x^{7} }}=\frac{1}{|x|.\sqrt[8]{ x^{7} }} \color{purple}{\frac{\sqrt[8]{ x }}{\sqrt[8]{ x }}} \\=\frac{\sqrt[8]{ x }}{|x^{2}|}\\---------------\)
2. \(\left(y^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{1}{3} . \frac{2}{3} }= y^{\frac{2}{9}}\\=\sqrt[9]{ y^{2} }\\---------------\)
3. \(\left(a^{\frac{-2}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{-2}{3} . \frac{4}{5} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
4. \(\left(x^{\frac{1}{5}}\right)^{1}\\= x^{ \frac{1}{5} . 1 }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
5. \(\left(x^{\frac{1}{6}}\right)^{\frac{-1}{3}}\\= x^{ \frac{1}{6} . (\frac{-1}{3}) }= x^{\frac{-1}{18}}\\=\frac{1}{\sqrt[18]{ x }}=\frac{1}{\sqrt[18]{ x }}. \color{purple}{\frac{\sqrt[18]{ x^{17} }}{\sqrt[18]{ x^{17} }}} \\=\frac{\sqrt[18]{ x^{17} }}{|x|}\\---------------\)
6. \(\left(x^{\frac{-5}{2}}\right)^{1}\\= x^{ \frac{-5}{2} . 1 }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
7. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
8. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-5}{4}}\\= a^{ \frac{-1}{2} . (\frac{-5}{4}) }= a^{\frac{5}{8}}\\=\sqrt[8]{ a^{5} }\\---------------\)
9. \(\left(x^{2}\right)^{\frac{5}{4}}\\= x^{ 2 . \frac{5}{4} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
10. \(\left(q^{\frac{5}{4}}\right)^{\frac{4}{5}}\\= q^{ \frac{5}{4} . \frac{4}{5} }= q^{1}\\\\---------------\)
11. \(\left(a^{\frac{5}{3}}\right)^{-1}\\= a^{ \frac{5}{3} . (-1) }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
12. \(\left(a^{1}\right)^{\frac{1}{2}}\\= a^{ 1 . \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)