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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{4}}\right)^{\frac{5}{3}}\\= q^{ \frac{-5}{4} . \frac{5}{3} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-1}{2} . \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
3. \(\left(x^{-2}\right)^{\frac{-2}{5}}\\= x^{ -2 . (\frac{-2}{5}) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
4. \(\left(a^{\frac{-4}{3}}\right)^{\frac{-1}{3}}\\= a^{ \frac{-4}{3} . (\frac{-1}{3}) }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
5. \(\left(x^{-1}\right)^{\frac{-1}{3}}\\= x^{ -1 . (\frac{-1}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
6. \(\left(q^{\frac{-4}{3}}\right)^{\frac{1}{6}}\\= q^{ \frac{-4}{3} . \frac{1}{6} }= q^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ q^{2} }}=\frac{1}{\sqrt[9]{ q^{2} }}. \color{purple}{\frac{\sqrt[9]{ q^{7} }}{\sqrt[9]{ q^{7} }}} \\=\frac{\sqrt[9]{ q^{7} }}{q}\\---------------\)
7. \(\left(a^{-1}\right)^{-1}\\= a^{ -1 . (-1) }= a^{1}\\\\---------------\)
8. \(\left(a^{\frac{1}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{1}{2} . \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
9. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-3}{5} . (\frac{-1}{2}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
10. \(\left(y^{\frac{-3}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-3}{2} . (\frac{-1}{2}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
11. \(\left(x^{\frac{-3}{4}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-3}{4} . (\frac{-1}{5}) }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
12. \(\left(y^{\frac{3}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{3}{2} . \frac{1}{2} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)