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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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