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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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