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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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