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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{3}}\right)^{\frac{2}{3}}\\= x^{ \frac{1}{3} . \frac{2}{3} }= x^{\frac{2}{9}}\\=\sqrt[9]{ x^{2} }\\---------------\)
2. \(\left(a^{\frac{2}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{2}{5} . \frac{1}{3} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
3. \(\left(y^{\frac{-3}{4}}\right)^{-1}\\= y^{ \frac{-3}{4} . (-1) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
4. \(\left(x^{\frac{3}{2}}\right)^{\frac{5}{3}}\\= x^{ \frac{3}{2} . \frac{5}{3} }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
5. \(\left(a^{\frac{-1}{6}}\right)^{1}\\= a^{ \frac{-1}{6} . 1 }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
6. \(\left(a^{\frac{-5}{2}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-5}{2} . (\frac{-3}{2}) }= a^{\frac{15}{4}}\\=\sqrt[4]{ a^{15} }=|a^{3}|.\sqrt[4]{ a^{3} }\\---------------\)
7. \(\left(x^{\frac{5}{6}}\right)^{\frac{-1}{4}}\\= x^{ \frac{5}{6} . (\frac{-1}{4}) }= x^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ x^{5} }}=\frac{1}{\sqrt[24]{ x^{5} }}. \color{purple}{\frac{\sqrt[24]{ x^{19} }}{\sqrt[24]{ x^{19} }}} \\=\frac{\sqrt[24]{ x^{19} }}{|x|}\\---------------\)
8. \(\left(y^{\frac{4}{3}}\right)^{\frac{-5}{6}}\\= y^{ \frac{4}{3} . (\frac{-5}{6}) }= y^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ y^{10} }}\\=\frac{1}{y.\sqrt[9]{ y }}=\frac{1}{y.\sqrt[9]{ y }} \color{purple}{\frac{\sqrt[9]{ y^{8} }}{\sqrt[9]{ y^{8} }}} \\=\frac{\sqrt[9]{ y^{8} }}{y^{2}}\\---------------\)
9. \(\left(q^{\frac{-5}{2}}\right)^{\frac{1}{4}}\\= q^{ \frac{-5}{2} . \frac{1}{4} }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
10. \(\left(y^{1}\right)^{\frac{-3}{5}}\\= y^{ 1 . (\frac{-3}{5}) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
11. \(\left(q^{\frac{-1}{5}}\right)^{\frac{4}{5}}\\= q^{ \frac{-1}{5} . \frac{4}{5} }= q^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ q^{4} }}=\frac{1}{\sqrt[25]{ q^{4} }}. \color{purple}{\frac{\sqrt[25]{ q^{21} }}{\sqrt[25]{ q^{21} }}} \\=\frac{\sqrt[25]{ q^{21} }}{q}\\---------------\)
12. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-5}{3}}\\= y^{ \frac{-2}{5} . (\frac{-5}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)