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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= a^{ \frac{-1}{2} . \frac{5}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
2. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-5}{6} . (\frac{-1}{2}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
3. \(\left(a^{\frac{-5}{3}}\right)^{1}\\= a^{ \frac{-5}{3} . 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
4. \(\left(y^{\frac{2}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{2}{5} . \frac{2}{3} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
5. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{3} . (\frac{-1}{5}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
6. \(\left(q^{\frac{-2}{3}}\right)^{\frac{5}{6}}\\= q^{ \frac{-2}{3} . \frac{5}{6} }= q^{\frac{-5}{9}}\\=\frac{1}{\sqrt[9]{ q^{5} }}=\frac{1}{\sqrt[9]{ q^{5} }}. \color{purple}{\frac{\sqrt[9]{ q^{4} }}{\sqrt[9]{ q^{4} }}} \\=\frac{\sqrt[9]{ q^{4} }}{q}\\---------------\)
7. \(\left(x^{1}\right)^{\frac{4}{3}}\\= x^{ 1 . \frac{4}{3} }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
8. \(\left(a^{\frac{-5}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{-5}{2} . \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
9. \(\left(y^{\frac{-5}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{-5}{3} . \frac{2}{5} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
10. \(\left(a^{\frac{1}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{6} . \frac{1}{2} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
11. \(\left(y^{-1}\right)^{\frac{1}{3}}\\= y^{ -1 . \frac{1}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
12. \(\left(q^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= q^{ \frac{2}{3} . (\frac{-3}{4}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)