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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-2}\right)^{-1}\\= q^{ -2 . (-1) }= q^{2}\\\\---------------\)
2. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-1}{6}}\\= a^{ \frac{-5}{3} . (\frac{-1}{6}) }= a^{\frac{5}{18}}\\=\sqrt[18]{ a^{5} }\\---------------\)
3. \(\left(a^{-1}\right)^{\frac{-1}{6}}\\= a^{ -1 . (\frac{-1}{6}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
4. \(\left(a^{1}\right)^{\frac{-1}{6}}\\= a^{ 1 . (\frac{-1}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
5. \(\left(x^{\frac{-1}{2}}\right)^{-2}\\= x^{ \frac{-1}{2} . (-2) }= x^{1}\\\\---------------\)
6. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-5}{4}}\\= a^{ \frac{-5}{6} . (\frac{-5}{4}) }= a^{\frac{25}{24}}\\=\sqrt[24]{ a^{25} }=|a|.\sqrt[24]{ a }\\---------------\)
7. \(\left(x^{\frac{-5}{4}}\right)^{\frac{1}{2}}\\= x^{ \frac{-5}{4} . \frac{1}{2} }= x^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ x^{5} }}=\frac{1}{\sqrt[8]{ x^{5} }}. \color{purple}{\frac{\sqrt[8]{ x^{3} }}{\sqrt[8]{ x^{3} }}} \\=\frac{\sqrt[8]{ x^{3} }}{|x|}\\---------------\)
8. \(\left(y^{\frac{4}{3}}\right)^{-2}\\= y^{ \frac{4}{3} . (-2) }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
9. \(\left(a^{\frac{-1}{3}}\right)^{-2}\\= a^{ \frac{-1}{3} . (-2) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
10. \(\left(x^{\frac{2}{3}}\right)^{-1}\\= x^{ \frac{2}{3} . (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
11. \(\left(a^{\frac{-1}{3}}\right)^{-1}\\= a^{ \frac{-1}{3} . (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
12. \(\left(q^{\frac{2}{5}}\right)^{\frac{-1}{5}}\\= q^{ \frac{2}{5} . (\frac{-1}{5}) }= q^{\frac{-2}{25}}\\=\frac{1}{\sqrt[25]{ q^{2} }}=\frac{1}{\sqrt[25]{ q^{2} }}. \color{purple}{\frac{\sqrt[25]{ q^{23} }}{\sqrt[25]{ q^{23} }}} \\=\frac{\sqrt[25]{ q^{23} }}{q}\\---------------\)