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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-1}{4}}\right)^{\frac{4}{3}}\\= q^{ \frac{-1}{4} . \frac{4}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\left(x^{\frac{2}{3}}\right)^{\frac{-5}{2}}\\= x^{ \frac{2}{3} . (\frac{-5}{2}) }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
3. \(\left(q^{\frac{-1}{2}}\right)^{-2}\\= q^{ \frac{-1}{2} . (-2) }= q^{1}\\\\---------------\)
4. \(\left(a^{\frac{-3}{5}}\right)^{1}\\= a^{ \frac{-3}{5} . 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
5. \(\left(x^{1}\right)^{\frac{1}{3}}\\= x^{ 1 . \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
6. \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\left(a^{\frac{5}{6}}\right)^{\frac{-1}{6}}\\= a^{ \frac{5}{6} . (\frac{-1}{6}) }= a^{\frac{-5}{36}}\\=\frac{1}{\sqrt[36]{ a^{5} }}=\frac{1}{\sqrt[36]{ a^{5} }}. \color{purple}{\frac{\sqrt[36]{ a^{31} }}{\sqrt[36]{ a^{31} }}} \\=\frac{\sqrt[36]{ a^{31} }}{|a|}\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{-3}{4}}\\= y^{ -1 . (\frac{-3}{4}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{5}{3}}\\= a^{ -1 . \frac{5}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
10. \(\left(a^{\frac{5}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{5}{2} . (\frac{-1}{2}) }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
11. \(\left(x^{\frac{3}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{3}{2} . (\frac{-1}{3}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\left(a^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{4}{3} . \frac{2}{3} }= a^{\frac{8}{9}}\\=\sqrt[9]{ a^{8} }\\---------------\)