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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-1}{4}}\right)^{\frac{3}{5}}\\= x^{ \frac{-1}{4} . \frac{3}{5} }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
2. \(\left(x^{\frac{2}{3}}\right)^{\frac{5}{3}}\\= x^{ \frac{2}{3} . \frac{5}{3} }= x^{\frac{10}{9}}\\=\sqrt[9]{ x^{10} }=x.\sqrt[9]{ x }\\---------------\)
3. \(\left(a^{\frac{-2}{5}}\right)^{-1}\\= a^{ \frac{-2}{5} . (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
4. \(\left(y^{-2}\right)^{\frac{-1}{2}}\\= y^{ -2 . (\frac{-1}{2}) }= y^{1}\\\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{2} . \frac{1}{6} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
6. \(\left(q^{\frac{-1}{5}}\right)^{\frac{5}{4}}\\= q^{ \frac{-1}{5} . \frac{5}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
7. \(\left(a^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{2} . (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
8. \(\left(q^{\frac{-1}{6}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-1}{6} . (\frac{-5}{3}) }= q^{\frac{5}{18}}\\=\sqrt[18]{ q^{5} }\\---------------\)
9. \(\left(a^{\frac{-3}{5}}\right)^{\frac{1}{3}}\\= a^{ \frac{-3}{5} . \frac{1}{3} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
10. \(\left(q^{\frac{5}{3}}\right)^{\frac{-1}{4}}\\= q^{ \frac{5}{3} . (\frac{-1}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
11. \(\left(y^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{-1}{3} . \frac{1}{2} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
12. \(\left(y^{\frac{3}{4}}\right)^{\frac{-3}{4}}\\= y^{ \frac{3}{4} . (\frac{-3}{4}) }= y^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ y^{9} }}=\frac{1}{\sqrt[16]{ y^{9} }}. \color{purple}{\frac{\sqrt[16]{ y^{7} }}{\sqrt[16]{ y^{7} }}} \\=\frac{\sqrt[16]{ y^{7} }}{|y|}\\---------------\)