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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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