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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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