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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{4}{5}}\right)^{\frac{-5}{3}}\\= x^{ \frac{4}{5} . (\frac{-5}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
2. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{2} . (\frac{-1}{5}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
3. \(\left(x^{\frac{4}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{4}{5} . \frac{1}{2} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
4. \(\left(y^{\frac{-1}{4}}\right)^{\frac{-1}{4}}\\= y^{ \frac{-1}{4} . (\frac{-1}{4}) }= y^{\frac{1}{16}}\\=\sqrt[16]{ y }\\---------------\)
5. \(\left(a^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{2} . (\frac{-3}{4}) }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
6. \(\left(a^{\frac{1}{3}}\right)^{\frac{4}{5}}\\= a^{ \frac{1}{3} . \frac{4}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
7. \(\left(x^{2}\right)^{\frac{5}{6}}\\= x^{ 2 . \frac{5}{6} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
8. \(\left(a^{\frac{-1}{6}}\right)^{\frac{-1}{5}}\\= a^{ \frac{-1}{6} . (\frac{-1}{5}) }= a^{\frac{1}{30}}\\=\sqrt[30]{ a }\\---------------\)
9. \(\left(q^{\frac{-1}{6}}\right)^{\frac{1}{2}}\\= q^{ \frac{-1}{6} . \frac{1}{2} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
10. \(\left(a^{\frac{5}{2}}\right)^{\frac{-1}{3}}\\= a^{ \frac{5}{2} . (\frac{-1}{3}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
11. \(\left(x^{1}\right)^{\frac{-3}{4}}\\= x^{ 1 . (\frac{-3}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
12. \(\left(y^{\frac{3}{4}}\right)^{\frac{3}{4}}\\= y^{ \frac{3}{4} . \frac{3}{4} }= y^{\frac{9}{16}}\\=\sqrt[16]{ y^{9} }\\---------------\)