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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{2}}\right)^{\frac{5}{4}}\\= y^{ \frac{-3}{2} . \frac{5}{4} }= y^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ y^{15} }}\\=\frac{1}{|y|.\sqrt[8]{ y^{7} }}=\frac{1}{|y|.\sqrt[8]{ y^{7} }} \color{purple}{\frac{\sqrt[8]{ y }}{\sqrt[8]{ y }}} \\=\frac{\sqrt[8]{ y }}{|y^{2}|}\\---------------\)
2. \(\left(x^{\frac{-4}{3}}\right)^{\frac{1}{4}}\\= x^{ \frac{-4}{3} . \frac{1}{4} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
3. \(\left(q^{\frac{2}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{2}{3} . \frac{3}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
4. \(\left(a^{\frac{-3}{5}}\right)^{-2}\\= a^{ \frac{-3}{5} . (-2) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
5. \(\left(y^{\frac{4}{5}}\right)^{2}\\= y^{ \frac{4}{5} . 2 }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
6. \(\left(a^{\frac{1}{3}}\right)^{\frac{5}{3}}\\= a^{ \frac{1}{3} . \frac{5}{3} }= a^{\frac{5}{9}}\\=\sqrt[9]{ a^{5} }\\---------------\)
7. \(\left(q^{-1}\right)^{2}\\= q^{ -1 . 2 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
8. \(\left(y^{\frac{-1}{4}}\right)^{\frac{4}{5}}\\= y^{ \frac{-1}{4} . \frac{4}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
9. \(\left(y^{\frac{1}{3}}\right)^{\frac{-4}{3}}\\= y^{ \frac{1}{3} . (\frac{-4}{3}) }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
10. \(\left(x^{-2}\right)^{1}\\= x^{ -2 . 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
11. \(\left(a^{\frac{5}{4}}\right)^{1}\\= a^{ \frac{5}{4} . 1 }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
12. \(\left(y^{\frac{1}{5}}\right)^{\frac{2}{5}}\\= y^{ \frac{1}{5} . \frac{2}{5} }= y^{\frac{2}{25}}\\=\sqrt[25]{ y^{2} }\\---------------\)