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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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