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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{5}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{2} . \frac{1}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
2. \(\left(y^{1}\right)^{\frac{-1}{5}}\\= y^{ 1 . (\frac{-1}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
3. \(\left(x^{\frac{-1}{6}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{6} . \frac{1}{2} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
4. \(\left(a^{\frac{-3}{4}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{4} . \frac{5}{4} }= a^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ a^{15} }}=\frac{1}{\sqrt[16]{ a^{15} }}. \color{purple}{\frac{\sqrt[16]{ a }}{\sqrt[16]{ a }}} \\=\frac{\sqrt[16]{ a }}{|a|}\\---------------\)
5. \(\left(q^{\frac{-5}{4}}\right)^{1}\\= q^{ \frac{-5}{4} . 1 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
6. \(\left(q^{2}\right)^{\frac{4}{3}}\\= q^{ 2 . \frac{4}{3} }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
7. \(\left(a^{\frac{4}{5}}\right)^{1}\\= a^{ \frac{4}{5} . 1 }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
8. \(\left(y^{\frac{1}{2}}\right)^{\frac{-1}{4}}\\= y^{ \frac{1}{2} . (\frac{-1}{4}) }= y^{\frac{-1}{8}}\\=\frac{1}{\sqrt[8]{ y }}=\frac{1}{\sqrt[8]{ y }}. \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y|}\\---------------\)
9. \(\left(q^{\frac{1}{6}}\right)^{\frac{4}{3}}\\= q^{ \frac{1}{6} . \frac{4}{3} }= q^{\frac{2}{9}}\\=\sqrt[9]{ q^{2} }\\---------------\)
10. \(\left(q^{\frac{-1}{2}}\right)^{-2}\\= q^{ \frac{-1}{2} . (-2) }= q^{1}\\\\---------------\)
11. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{1}{2} . (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\left(q^{\frac{-3}{2}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-3}{2} . (\frac{-5}{3}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)