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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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