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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{3}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{3}{5} . (\frac{-1}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
2. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-3}{4} . (\frac{-1}{4}) }= x^{\frac{3}{16}}\\=\sqrt[16]{ x^{3} }\\---------------\)
3. \(\left(a^{\frac{1}{3}}\right)^{\frac{1}{6}}\\= a^{ \frac{1}{3} . \frac{1}{6} }= a^{\frac{1}{18}}\\=\sqrt[18]{ a }\\---------------\)
4. \(\left(y^{\frac{-5}{4}}\right)^{-2}\\= y^{ \frac{-5}{4} . (-2) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
5. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= q^{ \frac{1}{2} . \frac{1}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= q^{ \frac{-1}{2} . (\frac{-1}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\left(q^{-1}\right)^{1}\\= q^{ -1 . 1 }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
9. \(\left(q^{1}\right)^{\frac{3}{5}}\\= q^{ 1 . \frac{3}{5} }= q^{\frac{3}{5}}\\=\sqrt[5]{ q^{3} }\\---------------\)
10. \(\left(x^{\frac{-2}{5}}\right)^{1}\\= x^{ \frac{-2}{5} . 1 }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
11. \(\left(q^{\frac{4}{3}}\right)^{\frac{4}{5}}\\= q^{ \frac{4}{3} . \frac{4}{5} }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
12. \(\left(a^{-2}\right)^{\frac{-3}{5}}\\= a^{ -2 . (\frac{-3}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)