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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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