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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{-4}{5} . (\frac{-1}{2}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
2. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{3}}\\= q^{ \frac{1}{5} . (\frac{-1}{3}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
3. \(\left(q^{\frac{5}{2}}\right)^{\frac{-1}{3}}\\= q^{ \frac{5}{2} . (\frac{-1}{3}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
4. \(\left(x^{\frac{-3}{4}}\right)^{1}\\= x^{ \frac{-3}{4} . 1 }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
5. \(\left(a^{-1}\right)^{\frac{1}{5}}\\= a^{ -1 . \frac{1}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
6. \(\left(q^{\frac{4}{5}}\right)^{\frac{4}{3}}\\= q^{ \frac{4}{5} . \frac{4}{3} }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
7. \(\left(x^{-2}\right)^{\frac{-2}{5}}\\= x^{ -2 . (\frac{-2}{5}) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
8. \(\left(a^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{2}{3} . (\frac{-3}{4}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
9. \(\left(a^{\frac{-5}{3}}\right)^{\frac{-3}{2}}\\= a^{ \frac{-5}{3} . (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
10. \(\left(y^{\frac{-2}{3}}\right)^{\frac{3}{2}}\\= y^{ \frac{-2}{3} . \frac{3}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)
11. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
12. \(\left(a^{\frac{-1}{2}}\right)^{\frac{2}{5}}\\= a^{ \frac{-1}{2} . \frac{2}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)