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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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