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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{2}}\right)^{\frac{2}{5}}\\= q^{ \frac{1}{2} . \frac{2}{5} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
2. \(\left(y^{-1}\right)^{\frac{-5}{6}}\\= y^{ -1 . (\frac{-5}{6}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
3. \(\left(a^{\frac{-1}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-1}{3} . \frac{2}{3} }= a^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ a^{2} }}=\frac{1}{\sqrt[9]{ a^{2} }}. \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a}\\---------------\)
4. \(\left(q^{\frac{-5}{6}}\right)^{\frac{-1}{6}}\\= q^{ \frac{-5}{6} . (\frac{-1}{6}) }= q^{\frac{5}{36}}\\=\sqrt[36]{ q^{5} }\\---------------\)
5. \(\left(q^{-1}\right)^{\frac{-1}{2}}\\= q^{ -1 . (\frac{-1}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
6. \(\left(q^{\frac{-1}{3}}\right)^{\frac{2}{5}}\\= q^{ \frac{-1}{3} . \frac{2}{5} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
7. \(\left(x^{-1}\right)^{\frac{1}{3}}\\= x^{ -1 . \frac{1}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(\left(a^{\frac{1}{5}}\right)^{-1}\\= a^{ \frac{1}{5} . (-1) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
9. \(\left(y^{\frac{-2}{3}}\right)^{\frac{1}{3}}\\= y^{ \frac{-2}{3} . \frac{1}{3} }= y^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ y^{2} }}=\frac{1}{\sqrt[9]{ y^{2} }}. \color{purple}{\frac{\sqrt[9]{ y^{7} }}{\sqrt[9]{ y^{7} }}} \\=\frac{\sqrt[9]{ y^{7} }}{y}\\---------------\)
10. \(\left(q^{-1}\right)^{\frac{5}{3}}\\= q^{ -1 . \frac{5}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
11. \(\left(y^{\frac{5}{2}}\right)^{\frac{-1}{4}}\\= y^{ \frac{5}{2} . (\frac{-1}{4}) }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}. \color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)
12. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)