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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-3}{2}}\\= y^{ \frac{-2}{5} . (\frac{-3}{2}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
2. \(\left(a^{\frac{-1}{4}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{4} . \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
3. \(\left(x^{\frac{-2}{3}}\right)^{\frac{1}{5}}\\= x^{ \frac{-2}{3} . \frac{1}{5} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
4. \(\left(x^{\frac{2}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{2}{5} . \frac{1}{2} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
5. \(\left(y^{-1}\right)^{\frac{5}{3}}\\= y^{ -1 . \frac{5}{3} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
6. \(\left(a^{-1}\right)^{\frac{2}{5}}\\= a^{ -1 . \frac{2}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
7. \(\left(a^{2}\right)^{\frac{-1}{5}}\\= a^{ 2 . (\frac{-1}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
8. \(\left(x^{\frac{1}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{1}{2} . \frac{3}{2} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
9. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-4}{3} . (\frac{-3}{2}) }= a^{2}\\\\---------------\)
10. \(\left(q^{1}\right)^{\frac{-1}{3}}\\= q^{ 1 . (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
11. \(\left(a^{\frac{5}{6}}\right)^{\frac{2}{3}}\\= a^{ \frac{5}{6} . \frac{2}{3} }= a^{\frac{5}{9}}\\=\sqrt[9]{ a^{5} }\\---------------\)
12. \(\left(q^{-2}\right)^{\frac{1}{2}}\\= q^{ -2 . \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)