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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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