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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{4}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{4}{3} . \frac{1}{3} }= y^{\frac{4}{9}}\\=\sqrt[9]{ y^{4} }\\---------------\)
2. \(\left(y^{1}\right)^{-1}\\= y^{ 1 . (-1) }= y^{-1}\\=\frac{1}{y}\\---------------\)
3. \(\left(a^{\frac{-1}{2}}\right)^{\frac{-4}{3}}\\= a^{ \frac{-1}{2} . (\frac{-4}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
4. \(\left(y^{1}\right)^{\frac{4}{3}}\\= y^{ 1 . \frac{4}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
5. \(\left(y^{\frac{-2}{3}}\right)^{\frac{2}{5}}\\= y^{ \frac{-2}{3} . \frac{2}{5} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
6. \(\left(x^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{3} . (\frac{-1}{2}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
7. \(\left(x^{1}\right)^{\frac{5}{2}}\\= x^{ 1 . \frac{5}{2} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
8. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{3}}\\= q^{ \frac{2}{3} . (\frac{-1}{3}) }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
9. \(\left(q^{\frac{-5}{4}}\right)^{-1}\\= q^{ \frac{-5}{4} . (-1) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
10. \(\left(q^{\frac{4}{3}}\right)^{\frac{-3}{5}}\\= q^{ \frac{4}{3} . (\frac{-3}{5}) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
11. \(\left(q^{\frac{1}{4}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{4} . \frac{5}{6} }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{\frac{1}{4}}\\= y^{ \frac{1}{2} . \frac{1}{4} }= y^{\frac{1}{8}}\\=\sqrt[8]{ y }\\---------------\)