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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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