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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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