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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{3}{4}}\right)^{\frac{1}{5}}\\= q^{ \frac{3}{4} . \frac{1}{5} }= q^{\frac{3}{20}}\\=\sqrt[20]{ q^{3} }\\---------------\)
2. \(\left(y^{1}\right)^{\frac{-2}{5}}\\= y^{ 1 . (\frac{-2}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
3. \(\left(y^{\frac{1}{4}}\right)^{\frac{-1}{2}}\\= y^{ \frac{1}{4} . (\frac{-1}{2}) }= y^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ y }}=\frac{1}{\sqrt[8]{ y }}. \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y|}\\---------------\)
4. \(\left(x^{\frac{-3}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{-3}{2} . \frac{3}{5} }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
5. \(\left(q^{\frac{-4}{3}}\right)^{1}\\= q^{ \frac{-4}{3} . 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{4}{3}}\\= y^{ \frac{-1}{2} . \frac{4}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
7. \(\left(q^{\frac{-1}{2}}\right)^{1}\\= q^{ \frac{-1}{2} . 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\left(y^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{3} . \frac{2}{3} }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
9. \(\left(x^{\frac{-4}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-4}{3} . (\frac{-2}{3}) }= x^{\frac{8}{9}}\\=\sqrt[9]{ x^{8} }\\---------------\)
10. \(\left(y^{\frac{1}{3}}\right)^{-1}\\= y^{ \frac{1}{3} . (-1) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
11. \(\left(x^{1}\right)^{\frac{-4}{5}}\\= x^{ 1 . (\frac{-4}{5}) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
12. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{4}}\\= a^{ \frac{2}{3} . \frac{1}{4} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)