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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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