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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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