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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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